Isotope effect of transport and key physics in the isotope mixture plasmas

The isotope effect of transport and key physics in isotope mixture plasmas is reviewed. Experiment, simulation, and theory discuss isotope mass dependence on confinement, transport, and turbulence. Experimental observation shows a wide variety of isotope mass dependence, due to the complicated process of determining the plasma confinement and transport and far from the simple mass dependence predicted by the gyro-Bohm model. The isotope effect directly influences the growth rate of instability and thermal diffusivity and indirectly influences confinement and transport property through other parameters. The isotope mixing is also described as key physics of isotope mixture plasma, essential to optimize fusion power in deuterium and tritium plasma.


Introduction
Although the ion species of future fusion plasma will be deuterium (D) and tritium (T), it is either hydrogen (H) or deuterium (D) in most of the current experiments, except for the DT one in TFTR and JET.Therefore, knowledge from a comparison between H and D plasma is essential to predict performance, especially transport characteristics in the D-T plasma.One of the key issues is the effective isotope mass (1 for H, 2 for D, and 2.5 for D-T plasma) dependence on global energy confinement and transport level (especially ion and electron thermal diffusivity).The issue is highlighted as an isotope effect study and has been investigated by experiment, simulation, and theory.The gyro-Bohm model, where the thermal diffusivity is proportional to the gyro-radius and square root of isotope mass, predicts better confinement for lighter isotope plasma.Because the isotope mass dependence predicted by the gyro-Bohm model is far from that observed in the experiment, understanding the mechanism determining the mass dependence is an urgent issue.In the gyro-Bohm model, the thermal diffusivity has a positive dependence of M 1∕2 (i.e., a negative dependence of global energy confinement time of M −1∕2 ).In contrast, the global energy confinement time has weak or positive dependence of M with  > 0 .
The isotope effect is one of the mysteries in a toroidal plasma and has been investigated in tokamak and helical devices (Bessenrodt-Weberpals et al. 1993;Maggi et al. 1999;Urano and Narita 2021;Tanaka et al. 2021;Osakabe et al. 2022).
The discrepancy between the gyro-Bohm model and experiment is due to the fact that many physics processes with different mass dependencies, determine the final transport and confinement.The assumption that the thermal diffusivity is proportional to the gyro-radius is too simplified as it ignores the various physics process in transport.Understanding the mass dependence for each physics process is essential, rather than simply investigating the mass dependence of thermal diffusivity finally determined.It should also be noted that the characteristics of the pedestal in the H-mode are restricted by MHD instability rather than transport.In contrast, the MHD instability does not play an essential role in L-mode plasma, where the transport determines the temperature and pressure gradients.Therefore, mass dependence has a wide variety, depending on the location (core or edge), transport state (L-mode, H-mode, and internal transport barrier), as well as the magnetic configuration (tokamak or helical plasma).
In spite of the complication of the isotope effect in toroidal plasma, its study has been done by a simple comparison with the same operational parameter between hydrogen and deuterium plasma.In order to understand the physics mechanism determining mass dependence, a more sophisticated comparison (profile matching, dimensionless analysis, threshold power to improved mode, zonal flow amplitude, etc.) is necessary.In this review paper, various physics processes are discussed in the category of a primary effect (direct) and secondary effect (indirect).Various approaches towards the comparison between different isotope masses are also discussed.A simple comparison study started from the first D-T experiment in the '90s, both for the core and pedestal, is discussed in Sect. 2. The comparison of profile matching with dimensional and non-dimensional parameters is described in Sect.3. The theoretical study for these comparison studies is followed in Sect. 4. In Sect.5, the primary and secondary focus on the impact of the gradient of electron density and impurity density are discussed.The power threshold for the transition to H-mode (also to ITB-plasma) is described in Sect.6.In Sect.7, the isotope mixing is also described as a critical physics in the isotope mixture plasma.

Primary and secondary isotope effects
The isotope effect on transport has been studied since the first deuterium-tritium experiment in the '90s.Despite intensive studies on this topic, the isotope effect has not been well understood.This is due to the fact that isotope effect on transport is not straightforward.Because the growth rate of turbulence has isotope mass dependence, the main isotope effect has been considered to appear directly at the turbulence level and then the thermal diffusivity in the heat transport and energy confinement time.In this review paper, any process having a direct effect to heat transport is called as one of the primary effects.However, various other isotope effects on particle transport and momentum transport affect the turbulence levels, as illustrated in Fig. 1.
There are several influences of isotope mass on other mechanisms, such as the convection of particles and impurity (Tanaka et al. 2016;Ida et al. 2019), neoclassical bipolar flux (Shaing et al. 2015), Reynolds stress (Hidalgo et al. 1999), and residual stress (Diamond et al. 2013) as primary effects to other transport channels.Therefore, density gradient, impurity density gradient, radial electric field E r , zonal flow, poloidal and toroidal velocity shear (and E r shear) may vary, depending on the isotope mass.These parameters strongly impact turbulence and thermal diffusivity, and the isotope effect through the change in these parameters is called a secondary isotope effect.The zonal flow and E r shear are essential parameters reducing the turbulence levels.However, the magnitude of zonal flow is strongly affected by the magnitude of the radial electric field, especially in the helical system.The combination of poloidal flow due to the Reynolds stress and toroidal flow due to the Residual stress determines the E r shear ( E × B shear) both in tokamak and helical plasmas.Due to the multiple paths (various mechanisms determining the turbulence), the isotope effect appears differently, depending on experiments and devices.These secondary isotope effects cause the complicated results of the isotope mass effect in the experiment and also the discrepancy between the observation and simple theoretical predictions.
It is well known that the isotope mass strongly impacts MHD stability and the characteristics of the pedestal (for example, pedestal width) (Saibene et al. 1999;Urano et al. 2012).The isotope mass alters the maximum pedestal pressure through Fig. 1 Diagram of primary and secondary isotope effects in toroidal plasma the ELM frequency in the H-mode plasma.The pedestal top temperature and density are boundary conditions of the transport in the core region.Therefore, a higher temperature at the pedestal top results in a large energy confinement time at the given transport in the core region.Here, the large ion gyro-radius of heavier ion species contributes to the broader pedestal width and higher pedestal temperature as a primary isotope effect.A higher pedestal top increases energy confinement time as a secondary effect.

Research approach for isotope effect study
There are various research approaches for a comparison study of transport in plasma with a different isotope mass.The matching parameters, adjusting parameters, and quantity of comparison of these approaches are summarized in Table 2. Here, q, B, I p , n e , P abs , P th , T e , T i , i , e , and E is a safety factor, magnetic field strength, plasma current, electron density, absorbed power, threshold power for the transition to improved mode, electron temperature, ion temperature, electron thermal diffusivity, ion thermal diffusivity, and global energy confinement time.Here, * , * , , Ω i , and M are the Larmor radius normalized by minor radius, electron-ion collision frequency normalized by the bounce frequency in a banana orbit, and plasma thermal pressure normalized by the pressure of a magnetic field ion cyclotron frequency and isotope mass, respectively.A simple comparison has proceeded with the same operation parameters, such as plasma current, magnetic field strength, the safety factor, electron density, and heating power.This comparison would be a good approach from an engineering point of view but not from one of physics.The electron and ion temperature profiles and derived electron and ion thermal diffusivity, and global energy confinement time are selected as quantities for comparison.
The other approaches are profile matching comparisons, either dimensional parameters (temperature and density) or non-dimensional ones (normalized gyro radius, collisionality, the ratio of kinetic energy to magnetic energy, so-called Fig. 2 Table of comparison of turbulence transport with different isotope mass values.In these analyses, the rotational transform, ∕2 (safety factor, q = 2 ∕ , in tokamaks), is usually fixed.The profile-matching comparisons are interesting even with dimensional parameters and give a deeper physics understanding than a simple comparison.Here, the particle fueling and heating are adjusted to match radial profiles of electron density and electron and ion temperature for the given safety factor q between different isotope mass plasma.(In many cases, particle fueling and heating location are fixed, and only the heating power is adjusted.)Then, the radial profiles of ion and electron thermal diffusivity, i , e , as well as energy confinement time, E , are compared.In contrast, the magnetic field strength, particle fueling and heating are adjusted to match the profile of non-dimensional parameters, * , * , , in the dimensionless analysis.Here the thermal diffusivity profiles normalized by ion cyclotron frequency, i ∕Ω i , e ∕Ω i are quantities for comparison.Dimensional pro- file matching is a good approach for comparison with the predictions of a simulation code, where the density and temperature profiles are input parameters.Non-dimensional profile matching is used when the thermal diffusivity is compared with the predictions of the gyro-Bohm model.Dimensionless analysis is a very good physics approach for the comparison of transport with different isotope mass plasma.
Since the isotope effect appears much more clearly as a difference in the power threshold to the transition to an improved mode, such as H-mode (ASDEX Team 1989) and the internal transport barrier (ITB) (Ida and Fujita 2018), comparison of transition power threshold is a very good approach for the isotope effect study.Here, heating power is scanned, and the threshold power for transition is a quantity for comparison.The magnitude of improvement by a transition above the threshold power can be another quantity for comparison.The ratios of ion and electron thermal diffusivities and energy confinement time after the transition to that beforehand are used as an improved factor.A more physics-based approach would be a comparison of turbulence contributing to the transport in a plasma with a different isotope mass.Zonal flow or fluctuation with long-range correlation is a key parameter, and a comparison of turbulence-driven radial flux is desirable.Direct measurements of zonal flow in the plasma with different isotope masses is an excellent physics approach for studying the isotope effect but requires sophisticated turbulence diagnostics.

Global energy confinement time
The isotope effect on global energy confinement time, E , depends on the confinement regime.For example, the isotope effect is strong ( E ∝ A 0.85 ) in a peaked-den- sity supershot regime and an H-mode one but weaker ( E ∝ A 0.5 ) in beam-heated L-mode plasmas with a broad density profile and no isotope effect on global confinement time is observed in ohmic plasma, reverse shear plasma and enhanced reverse shear plasma in TFTR (Scott et al. 1995(Scott et al. , 1996)).
The engineering parameter scaling of the thermal energy confinement time, th for ELMy H modes, based on the ITER multi-machine database, has the form (Gibson and JET Team 1998) 23 Page 6 of 42 The dataset isotope (tritium, deuterium, and hydrogen) experiment in JET provides new isotope mass dependence.As seen in Fig. 3a, the dataset to pairs of discharges in deuterium, tritium and hydrogen in which the density and power levels are close (powers within 5% and densities within 25%) has a good agreement with 1.03 ITERH−EPA97(y) (M∕2) −0.17 (Cordey et al. 1999).Then, we find that the mass depend- ence of the energy confinement time is weak as This weak mass dependence is consistent with the TFTR results where only a tiny improvement ( ∼10% in global energy confinement time of the thermal plasma) is seen between hydrogen and deuterium discharges (Barnes et al. 1996).Although the mass dependence of the energy confinement time is very small, the pedestal kinetic energy W ped [∼ 2 2 Ra 2 n ped T ped ] has strong mass dependence of Therefore, the mass dependence of the energy confinement time tends to be strong as the fraction of pedestal kinetic energy to total kinetic energy increases.The isotope effect varies, depending on the wall condition, such as carbon (C), tungsten (W), or nickel (Ni) walls.In plasma with an ITER-like wall in JET, the dependence of global energy confinement time on isotope mass is found to be weak in L-mode plasma ( A 0.15 ) but relatively strong in type I ELMy H-mode plasma ( A 0.4 ) (Joffrin et al. 2019).
(1) ITERH−EPA97(y) = 0.029I 0.90 B 0.20 P −0.66 n 0.40 R 2.03 0.19 0.92 M 0.2 (2) th (core) ∝ M 0.03±0.1 (3) th (pedestal) ∝ M 0.96 Fig. 3 Global energy confinement time as a function of ITER-EPS97(y) scaling for hydrogen (H), deuterium (D), and tritium (T) ELMy plasma in JET and as a function of the loss of power for hydrogen and deuterium H-mode plasma in JT-60U (from Fig. 2 in Cordey et al. (1999) and Fig. 1 in Urano et al. (2012)) Figure 3b shows that the th value decreases continuously with the loss of power P L , for both hydrogen and deuterium in JT-60U (Urano et al. 2012).The empirical power law expects a magnitude of decrease of th ∝ P −0.69 .However, the thermal energy confinement time th for deuterium plasma is larger than that for hydrogen by a factor of 1.2-− 1.3 at a given P L .This corresponds to the mass dependence of ∝ M 0.3 , which is much stronger than that observed in JET.The grey line indicates the constant thermal stored energy with W th = 0.75 MJ in the steady state phase.For example, the loss of power to sustain the plasma with 0.75 MJ is 4 MW and 8 MW for deuterium and hydrogen plasma, respectively.The heating power required for hydrogen plasma is double that for deuterium plasma to produce plasma with the same kinetic energy.A strong isotope mass dependence in the pedestal is found, which is enhanced at high gas puffing in ASDEX.This is because of the ELM type changes from D to H for matched engineering parameters, likely due to differences in the inter-ELM transport with isotope mass (Schneider et al. 2022).

Core region: mass dependence of transport
The isotope effect study was stated at the first deuterium-tritium (DT) experiments performed in the '90s (Hawryluk et al. 1994;Keilhacker et al. 1999).The DT experiment in TFTR and JET in the '90s demonstrated higher plasma parameters (ion temperature and total pressure) for DT discharge than DD discharge, as seen in Fig. 4. The critical question was whether the higher plasma parameters in the DT discharge were attributed to the contribution of energetic alpha particles produced by the fusion reactions and additional alpha particle heating.Although the isotope effect (better confinement in DT plasma than in DD plasma) was reported from the TFTR experiment, the net isotope effect on energy confinement was concluded to be negligible, from a detailed analysis using transport code in JET.It should be noted Fig. 4 Radial profiles of ion temperature measured for DD discharge (open squares) and DT discharge (closed circles) in TFTR with a heating power of ∼ 30 MW, and total pressure for DD discharge (#40305) and DT discharge (#42676) at the same plasma current (3.8 MA) and heating power ( ∼ 23 MW) in JET.Here, the plasma current for the highest fusion power discharge (#42976) is 4.2MA.(from Fig. 2a in Hawryluk et al. (1994) and Fig. 5 in Keilhacker et al. (1999)) that the isotope effect varies, depending on the confinement regime as discussed in Sect.2.1.
In TFTR, the ion temperature measured with charge exchange spectroscopy was 20-25% higher in the DT discharge than that in the DD ones.The larger ion temperature gradient in the core region is due to the reduction of ion thermal diffusivity in the core of DT plasma.Here, the vertical lines indicate the position of the magnetic axis for DD discharge (dashed line) and DT discharge (solid line).The magnetic axis for the DT discharge moves slightly outward due to the larger Shafranov shift, which shows larger pressure for DT discharge.The heating power by NBI (beam injection power), alpha particle and fusion power produced by the DD or DT fusion reactions is 29.7, 0, 0.044 MW in DD discharge and 29.5, 0.86, 6.2 MW ( ∼ 20% of total heating power) in DT discharge, respectively.The contribution of alpha heating to the total heating power is only 1-2% and is negligible.The volume-integrated total kinetic energy of the electron, ion, beam, and alpha particles is 1.04, 1.36, 1.98, and 0 MJ in the DD discharge and 1.17, 1.64, 2.21, and 0.14 MJ in the DT discharge, respectively.The electron, ion, and beam kinetic energy in the DT discharge is 13, 21, and 12% higher than that in the DD discharge for the same heating power, which indicates an isotopic effect on ion energy confinement is most significant in this experiment.
In JET, the total pressure computed by the transport code, TRANSP, is larger in the DT discharge (#42676) than that in the DD, one (#40305), especially near the plasma magnetic axis ( = 0).By increasing the plasma current from 3.8 to 4.2 MA, the pressure also increases, as seen in the DT discharge (#42976).In this DT discharge, the total heating power (by NBI and ICRF), alpha particle, and fusion power produced by the DT fusion reactions is 23.5, 1.62, and 14.2 MW ( ∼ 60 % of total heating power), respectively.Deuterium-tritium simulations using the TRANSP code have been made for a DD discharge (#40305), assuming transport coefficients estimated from the DD discharges, i.e., neglecting isotopic effects but including heating by an alpha particle.The radial profiles of alpha particle pressure and the total pressure profile evaluated by deuterium-tritium simulations are indicated by the #40305 simulation.Here, thermal diffusivities are kept constant in the simulation, going from DD to DT.The total pressure of the #40305 DT simulation is slightly larger than that of the DT discharges with the same current (#42676).These slight differences would be due to the power degradation of confinement (an increase of thermal diffusivities associated with the increase of heating power due to alpha particle heating (7% of total heating power) which is not taken into account in this simulation.These results confirm that no isotope effect of confinement was observed between the DD and DT discharges.Therefore, the difference in pressure profiles between the DD discharge (#40305 ) and DT discharges (#42676) is due to the difference in the population of alpha particles produced by the nuclear fusion reactions.These observations demonstrate that the net isotope effect on energy confinement is negligible.The discrepancy between TFTR and JET results is due to the difference in analysis (treatment of alpha particle effect), because the improvement of ion temperature T i (DT)∕T i (DD) in TFTR is similar to that of total pressure p tot (DT, #72676)∕p tot (DD, #70305) in JET.In JET analysis, the pressure increase is due to the influence of alpha particles, which is ignored in TFTR analysis.This discrepancy demonstrates the difficulty in extracting the isotope mass effect on confinement by comparing DD and DT discharge.
Transport analysis in plasma with different isotope species was applied to evaluate ion thermal diffusivity as an indicator of the isotope effect on core transport.Significant differences in the isotope effect were found in three big tokamaks, TFTR, JET, and JT-60U.Figure 5a, b shows the radial profiles of ion thermal diffusivity from TRANSP before and after the L-H transition for the DD and DT H-mode discharges in TFTR (Bush et al. 1995).In the DD plasma, the ion thermal diffusivity is only slightly reduced after the transition from L-mode to H-mode.In contrast, a significant reduction of ion thermal diffusivity (by a factor of 3 at r/a = 0.7) is observed after the transition to H-mode in the DT plasma.Therefore, the isotope effect (reduction of thermal diffusivity in the DT plasma) is weak in the L-mode plasma but significantly strong in the H-mode one.In contrast, the i of the deuterium and tritium discharges become similar towards the edge region in the JET H-mode plasmas.As seen in Fig. 5c, the ion thermal diffusivity i of a tritium discharge is even larger than that of a deuterium discharge in the core region (Cordey et al. 1999).Since global energy confinement is mainly contributed by edge transport, the no isotope effect in the global energy confinement is observed in JET.A tritium neutral beam is injected into the tritium plasma in the tritium discharge, and a deuterium neutral beam is injected into the deuterium plasma in the deuterium discharge.The plasma current, electron density, and heating power are similar for these two discharges ( I p = 1 MA, P NBI = 5.3 MW, and 2.4 × 10 19 m −3 ).The mass dependence of ion thermal diffusivity observed in JET is inconsistent with that observed in TFTR H-mode plasmas.The ion thermal diffusivity increases in the core while it decreases at the edge as the isotope ion mass increases in JET.It is in contrast to the ion thermal diffusivity decreases in the whole plasma region as the isotope ion mass increases in TFTR.
In JT-60U, a comparison of ion thermal diffusivity between hydrogen and deuterium plasmas was performed with similar NBI heating power ( P NBI = 8.0 MW for hydrogen plasma and P NBI = 7.4 MW for deuterium plasma (Urano et al. 2012).Although the ion temperature was higher for the deuterium plasma than for the hydrogen plasma, this was mainly attributed to the larger ion heat flux Q i for deute- rium plasma.The accelerating energy of NBI, E NBI , of 85 keV was below or com- parable to the critical energy, E c , defined as the energy threshold at which thermal ions and electrons are equally heated (Stix 1972).More than 75% of the total heating power contributes to ion heating in JT-60U.The critical energy E c tended to increase for larger beam ion mass and higher impurity concentration.In this experiment, the heating power to ions and resultant Q i value was higher for deuterium than for hydrogen ( Q i for deuterium is 23 % higher than Q i for hydrogen at r∕a = 0.6).As seen in Fig. 5d, the radial profiles of i are nearly identical between hydrogen and deuterium plasma.

Pedestal region in the H-mode plasma: impact of MHD stability
The difference in mass dependence between core ( M 0.03 ) and pedestal ( M 0.96 ) described above indicates that the mechanism determining temperature T and density gradient n is different between core and pedestal.The transport process in the core region usually determines the T and n gradients.In contrast, MHD stability determines the T and n at the pedestal top in ELMy H-mode plasma.In the H-mode, the thickness of the strong radial electric field shear layer is determined by the orbit loss and magnitude of poloidal viscosity and is ∼ 1.5 times the poloidal ion gyro-radius (Ida et al. 1990(Ida et al. , 1994)).Based on the E × B shearing suppression of the edge turbu- lence, the pedestal width is predicted to be scaled as pi , while ideal MHD limits the pedestal gradient.Here, pi is the poloidal ion gyro-radius, and is between 0.5 and 1 depending on the model (Urano 2014).This is the case, especially in spherical tokamaks, and the pedestal stability depends critically on resistive and kinetic effects.Therefore, higher maximum pressure at the top of the edge pedestal is predicted in the deuterium plasma, where the ion gyro-radius is 1.4 times that of the hydrogen plasma.Because the MHD stability, rather than the confinement, determines the maximum pedestal pressure in the ELMy H-mode, the strong mass dependence of pedestal pressure is one of the secondary isotope effects.Maximum pedestal density and temperature (n-T diagram) are investigated for plasma with different isotope species.As seen in Fig. 6a, higher pedestal pressures are obtained as the isotope mass increases from hydrogen to deuterium and tritium (Saibene et al. 1999).Here, full symbols represent the data for 2.6 MA/2.7 T in hydrogen, deuterium, and tritium, and open symbols represent the data for 1.7 MA/1.7 T in hydrogen and 1.8 MA/1.8 T in deuterium in JET.Maximum pedestal pressures increase as the plasma current increases with a constant safety factor of q.The increase of a maximum pedestal pressure with larger mass is much more significant than expected by the increase of pedestal width, which is proportional to the square root of the mass.
The isotope mass also has a strong influence on the ELM frequency.As seen in Fig. 6b, the ELM frequency increases with the net power crossing the separatrix P sep , both for hydrogen (H) and deuterium (D) plasma with different gas feeds (dia- mond: low gas, triangles: medium gas, squares: high gas) (Horvath et al. 2021).The ELM frequency in the plasma with medium gas is 60-90 kHz for hydrogen plasma (red triangles) and 40-50 kHz for deuterium plasma (blue triangles).At the given P sep of 7 MW, the ELM frequency of hydrogen plasma is 1.5 times that of deute- rium plasma.Figure 6c shows the pedestal top density as a function of f ELM in low (= 0.2) H (red) and D (blue) plasmas for 1.0 MA/1.0 T discharge (open triangles) and 1.4 MA/1.7 T discharge (closed circles).The ELM frequency becomes low for larger plasma currents.H and D pedestals at similar f ELM (but different P sep ) have comparable pedestal densities, as highlighted by the black dashed circles.This result suggests that the isotope effect observed in the ELMy H-mode is attributed to the isotope effect of MHD stability, rather than the isotope of transport.In other words, the ELM frequency is more important in determining the pedestal top density rather than the pedestal transport.Because the pedestal top density decreases as the ELM frequency is increased, the former becomes higher at similar P sep .
Similar results are reported from JT-60U, as seen in Fig. 6d-f (Urano et al. 2012).Here, triangles and circles indicate the data for hydrogen and deuterium plasmas, respectively.Figure 6d shows the pedestal n-T diagram in the cases of hydrogen and deuterium plasmas performed at plasma current I p = 1 MA, toroidal magnetic field strength, B T = 2 T and absorbed power, P abs = 8-9 MW in JT-60U.Triangles and circles indicate the data for hydrogen and deuterium plasmas, respectively.Broken curves show a constant electron pressure of 1.5 and 3.0 kPa.The pedestal top temperature and pressure in the deuterium plasma are twice those in the hydrogen plasma.Similar to the JET results, the ELM frequency increases as the separatrix P sep does, and the ELM frequency of hydrogen plasma is 1.5 times that of deute- rium plasma.These results in JT-60U show that both decreases in ELM frequency and reduction of transport contribute to increased edge temperature and pressure.In this case, both isotope effects on MHD stability and transport are comparably important.The data points (A) and (B) indicate a pair of plasmas at a given stored energy.Higher pressure at the top of the pedestal results in a larger thermal energy confinement time in deuterium plasma, as seen in Fig. 6f.Hydrogen plasmas at P abs < 5 MW with no clear signature of type-I ELM activity are shown as grey triangles.

Profile matching
There are two approaches to comparing transport in the isotope effect study.One is the comparison of temperature and pressure profiles between plasma with different isotope species with the same electron density, heating power, and configuration parameters.The other is the comparison of heating power (and thermal diffusivity) between plasma with different isotope species with the same dimensional parameters (temperature, density, magnetic field) or non-dimensional ones (normalized gyro-radius, collisionality, and pressure).In the former comparison study, only line averaged electron density is adjusted.In contrast, the heating power (and also the magnetic field in the case of non-dimensional analysis) should be adjusted to match the dimensional or non-dimensional parameters in the latter comparison (profile matching).

Dimensional analysis
Isotope effect studies for ion and electron transport with dimensional profile matching were investigated in JT-60U and the LHD, respectively.Figure 7a, b shows the radial profiles of ion temperature, T i , and the ion thermal diffusivity, i , for hydro- gen and deuterium plasma with very similar electron temperature and thermal pressure profiles (Urano et al. 2012).In this experiment, the profiles of the electron temperatures are also very similar.In the figure, the radial profiles of electron temperature T i become identical within the error bar of the measurements.To match the ion temperature profile, the required heating power for hydrogen is two times that for deuterium.The source heat flux of ions is responsible for nearly 40% of the total in both cases.The i values for hydrogen are explicitly higher throughout the minor radius than those for deuterium, which is consistent with the factor two of differences in global energy confinement time, plotted in Fig. 3 (A, B show data for deuterium and deuterium plasma, respectively).These experimental results demonstrate the better confinement of deuterium plasma.
Figure 7c, d shows the radial profiles of electron temperature, T e , and the electron thermal diffusivity, e , for hydrogen and deuterium plasma with approximately the same line-averaged electron density ∼ 2.4 × 10 19 m −3 (Takahashi et al. 2018).The magnetic configuration was identical both for the H and D plasmas (magnetic axis R ax = 3.6 m and magnetic field strength B t = 2.705 T).Although the line-averaged electron density was fixed as ∼ 2.4 × 10 19 m −3 , the the electron density in the core region (0.2 < r eff ∕a 99 < 0.6 ) was 20 % higher for the deuterium plasma.The elec- tron temperature profile in the deuterium plasma was identical to that of the hydrogen plasma.However, the heating power of ECRH was lower in deuterium plasma (3.95 MW for hydrogen discharge and 3.09 MW for deuterium discharge).The drop of the electron thermal diffusivity at r eff ∕a 99 < 0.45 observed in both the hydrogen and the deuterium plasma was due to the formation of the electron internal transport barrier.Figure 7d clearly shows that e is lower in deuterium plasma by a factor of two in the core region, which is consistent with the results in JT-60U.

Dimensionless analysis
Dimensionless analysis has been applied in JET and the LHD.The radial profiles of dimensionless effective thermal diffusivity are plotted in Fig. 8.The dimensionless effective thermal diffusivity is given by M ∕B or ∕Ω i , where M is the ion mass and Ω is the ion cyclotron frequency, defined as eB/M of bulk ion (B is magnetic field strength and e is the elementary charge).In this analysis, heating power, plasma density, and magnetic field are adjusted to match the radial profile of the Larmor radius normalized by minor radius, * [= i ∕a] , electron-ion collision frequency normalized by the bounce frequency in a banana orbit, * [= ei ∕ b ] , and plasma thermal pressure normalized by the pressure of a magnetic field, , between hydrogen and deuterium plasma.Figure 8a, b shows the radial profiles of dimensionless effective thermal diffusivity for the ELMy H-mode and L-mode isotope identity pair in hydrogen (H) and deuterium (D) discharges, respectively, in JET (Cordey et al. 2000;Maggi et al. 2019).The profiles of the dimensionless effective thermal diffusivity, M eff ∕B , for the ELMy H-mode, are almost identical near the edge region r/a = 0.9 but show slight differences in the central region.The dimensionless effective thermal diffusivity ( M eff ∕B ) for deuterium plasma is lower than that for hydrogen plasma.In both L-mode and H-mode plasmas, the dimensionless effective thermal diffusivity is very similar in hydrogen and deuterium plasma within experimental uncertainties.
Figure 8c, d shows the comparison of electron and ion thermal diffusivities in dimensionally similar plasmas where the normalized Larmor radius, collisionality, and plasma beta between hydrogen and deuterium plasma are identical (Yamada et al. 2019).The normalized electron thermal diffusivity is significantly lower for deuterium plasma than for hydrogen plasma, considering the error range.In contrast, deuterium plasma's normalized ion thermal diffusivity is only slightly lower than that of hydrogen plasma.The reduction of ion transport is less than that of electron transport.
The reduction of heat diffusivity is seen in the entire plasma, compensating for degradation due to the gyro-Bohm factor in the energy confinement.Figure 8e shows the ratio of normalized thermal diffusivity at = 2∕3 , as a function of the collisionality.It is seen that the ratio of electron thermal diffusivity is at around 0.5, implicating the isotope effect of M −1 .In contrast, the ratio of ion thermal diffusivity shows a different trend.Although the ratio is less than unity in a low collisionality regime, it approaches unity in a higher collisionality one.The possible reason for this collisionality dependence is the change in dominant turbulence across the range of collisionality.The transition from a TEM dominant turbulence state to an ITG one associated with the increase of collisionality was reported at the LHD (Ida et al. 2020(Ida et al. , 2021)).The clear reduction of thermal diffusivity, in particular, in the electron heat transport, is consistent with the reduction of thermal diffusivity for the dimensional profile matching experiment plotted in Fig. 7d.

Isotope mass dependence
When the isotope effect on the turbulent transport is examined, one should care about the mass dependence resulting from the gyroBohm diffusivity.The isotope mass dependence looks different depending on whether the mass-dependent or mass-independent normalization is considered for the growth rate and poloidal wavenumber.
Based on a mixing length estimation, the turbulent diffusivity for different isotope masses can be expressed as (Kadomtsev 1965) where γs and k⟂s is the normalized linear growth rate and the wavenumber defined as γs = a∕v ts and k⟂s = k ⟂ ts , respectively.Here, v ts and ts are the thermal speed and gyro-radius of each isotope ion with s = H, D, T and a is the minor radius of plasma.
From the mixing-length argument, the linear growth rate ( ∼ a∕v ts ) becomes smaller for heavier ions, as ∝ M −1∕2 due to lower thermal speed when the ion temperature is identical between the different isotopes.Due to the larger gyro-radius, the wavenumber of ion-scale unstable modes ( ∼ 1∕ ts ) should be smaller for the heavier ions, as ∝ M −1∕2 .Therefore, the normalized linear growth rate γs and normalized wavenum- ber k⟂s are useful to extract the mass dependence on microinstability and turbulent transport.When the normalized linear growth rate and wavenumber have no mass dependence, the turbulent diffusivity, turb , indicates a mass dependence of M 1∕2 which is called gyro-Bohm dependence typically observed for ion gyro-radius-scale turbulence.
The turbulence is suppressed by the radial shear of the mean E × B flow, V E×B (r) .The ratio of shearing rate, E×B ( ∼ dV E×B (r)∕dr ), to the growth rate, (k) , is the key parameter determining the suppression effect.The typical time-scale of the instability growth becomes smaller for heavier isotope due to the slower thermal velocity by M 1∕2 .The shear flow stabilization acts relatively stronger on such slower linear modes in the given shearing rate, which is mass-independent.The turbulent diffusivity for different isotope masses can be modified as (Weisen et al. 2020 where is a parameter describing the strength of shear flow stabilization.This formula predicts the positive mass dependence of turbulent diffusivity of M 1∕2 when the E × B flow shear is weak, which contradicts the negative mass dependence of turbulent diffusivity observed in an experiment.As E × B flow shear increases, tur- bulent diffusivity decreases due to the shear flow stabilization effect, which becomes stronger for plasma with a larger isotope mass. Here, a mixed-length diffusion model was described, based on a picture of turbulent diffusion, but it does not adequately describe the electron-scale turbulent transport.This is because of the formation of an eddy structure called "Streamer" ( k r ∼ 0, k ∼ 1∕ e ), which extends radially well beyond the e scale in ETG turbulence, as indicated by the gyrokinetic calculations for electron scale turbulence (Dorland et al. 2000;Jenko et al. 2000).There is no definitive mixed-length diffusion model for electron-scale turbulence, valid under various parameters.Further study with experimental measurements of electron-scale fluctuations is necessary.This paper emphasizes discussing the mixed-length diffusion model on ion-scale turbulence.
The theoretical study of the isotope effect started from the '90s by calculating the growth rate of various instability modes as a function of mode number (Dong et al. 1994;Lee and Santoro 1997;Tokar et al. 2004).The influence of isotope mass on micro-instability driving the turbulence has been studied using the gyro-kinetic simulation codes of GYRO, GENE, and GKV (Pusztai et al. 2011;Garcia et al. 2017;Nakata et al. 2016).Recently a new quasilinear saturation model SAT3 has been developed to calculate turbulent radial fluxes in the core of tokamak plasmas (Dudding et al. 2022).Figure 9a shows the growth rate of the ion temperature gradient (ITG) mode as a function of poloidal wavenumber k H , calculated for pure hydrogen (H), deuterium (D), tritium (T), and isotope mixture plasma, based on the gyrokinetic integral equation (Dong et al. 1994).The growth rate is normalized with the phase speed of electron drift wave, * e ∕k H , to directly compare the ion-mass effects on the growth rate for the different isotope plasmas.Here, k , H , and * e are the poloidal wavenumber, gyro radius of a hydrogen ion, and electron diamagnetic drift frequency, respectively.The maximum growth rate is lowest (less unstable) for the tritium plasma and highest (most unstable) for the hydrogen plasma.A deuterium plasma has a maximum growth rate with a magnitude in between hydrogen and tritium.The maximum growth rate of the mode is inversely proportional to the square root of the ion mass number, indicating gyroBohm-like mass dependence.A similar mass dependence of the maximum growth rate is predicted of the dissipative trapped electron (DTE) modes, as seen in Fig. 9b (Tokar et al. 2004).The growth rate is calculated by considering finite gyro radius effects in the analysis of the ion response to perturbations.The peak wave number � to the maximum growth rate max decreases with increasing isotope mass.Here, p is the gyro radius of a proton.The peak real frequency r,max corresponding to the maximum growth rate also decreases with increasing isotope mass.Figure 9c, d show the normalized growth rate, R ax ∕v ts , (solid lines) and the mode frequency, R ax ∕v ts , (dashed lines) for ITG instability and trapped electron mode (TEM) instability, as a function of the normalized wavenumber k y ts (Nakata et al. 2016).As seen in Fig. 9c, the growth rate normalized with a thermal speed of each ion species, s, is identical even for a different ion species for ITG instability.The GyroBohm-like mass dependence of the ITG growth rate can be seen more apparently when the species(or mass)-dependent normalization is applied to the growth rate and wavenumber.It should be noted that the difference between Fig. 9c and Fig. 9a is due to the normalization by the parameter of each isotope ion or hydrogen ion, which gives the difference of the x-and y-axes by a factor of the root of the square of the mass.The x-and y-axes in Fig. 9c is k⟂s and γs , respectively, while the x-and y-axes in Fig. 9a is k ⟂ and , respectively.The results plotted in The weakly collisional TEM is examined by a gyrokinetic calculation with fully gyrokinetic ions and electrons in a real mass ratio (Nakata et al. 2016).
The TEM's maximum normalized growth rate decreases for the heavier isotope ions, although the mode frequency does not depend on the isotope mass in speciesdependent normalization.The mass dependence of this normalized growth rate γs is close to M −1∕2 at given k⟂s , which is canceled by the mass-dependence of the root of the square, M 1∕2 in Eq. ( 4).Turbulent thermal diffusivity is expected to be weak iso- tope mass dependence, which could be consistent with the mass dependence of core transport, observed in the experiment.The strong isotope dependence found in the TEM is attributed to finite electron-ion collisions.The isotope effects on electronscale instability are also investigated, where the wavenumber spectra of and r , normalized by the electron thermal speed v te , and the gyro-radius te in the TEM- ETG regimes, are shown in Fig. 9e.In the present analyses, the stabilization effects due to T e ∕T i > 1 and the finite Debye length lead to a near-marginal ETG instability with a moderate growth rate.The ETG growth rate has two peaks at k y te = 0.1 and 0.175 and the mass dependence in the isotope effect is weak.

Collisionality dependence
In order to estimate the impacts of isotope ion mass on turbulent transport levels, linear and nonlinear analyses are performed by an electromagnetic gyro-kinetic Vlasov code GKV (Watanabe and Sugama 2006;Watanabe et al. 2008) with multiple-particle-species treatment (Nakata et al. 2015).Figure 10a shows the collisionality dependencies of the radial heat flux, Σ s=i,e q s for hydrogen (H), deuterium (D), and tritium (T) plasmas, determined by linear (labeled L-) and nonlinear (labeled NL-) calculation (Nakata et al. 2017).Here, Σ s=i,e q s is the total ion and electron heat flux, defined as n s a s g dT s ∕d and n s , a, s , and g is ion (s = i) and electron (s = e) density, the minor radius, ion (s = i) and electron (s = e) thermal diffusivity, and the geometric factor, respectively.The radial flux driven by ITG instability is nearly independent of ion-ion collisionality, ii and shows the gyro-Bohm type ion mass dependence of the square root of the mass ( Σ s=i,e q s (H) < Σ s=i,e q s (D) < Σ s=i,e q s (T) ).In contrast, the radial flux driven by TEM instability decreases significantly as the electron-ion collisionality, ei , increases by the collisional stabilization effect.The gyro-Bohm type ion mass dependence is also seen in the collisionless limit of TEM, the reversal ion mass dependence ( Σ s=i,e q s (H) > Σ s=i,e q s (D) > Σ s=i,e q s (T) ) appears at higher collisionality due to the stronger collisional stabilization for heavier isotope ions.The radial heat flux calculated with a non-linear TEM also shows the reversal ion mass dependence ( Σ s=i,e q s (H) > Σ s=i,e q s (D)).
The characteristics of collisional dependence of the radial flux driven by ITG and TEM instability plotted in Fig 10a are not unique features in the magnetic field configuration in the LHD.Similar characteristics are seen in the radial flux of a Cyclone-Base-Case (CBC)-like tokamak configuration (Dimits et al. 2000).Figure 10b, c show very weak collisionality dependence of heat flux for ITG instability and strong (even stronger than that for the LHD configuration) collisionality dependence for TEM instability.A reasonable agreement is seen between the linear and non-linear calculations.Comparisons of the entropy transfer (Nakata et al. 2012) have identified the reduction of radial flux by enhanced zonal flow (ZF).
The linear results are uniformly scaled for a qualitative comparison of profiles.The open symbols also display NL-TEM cases without the zonal flow.The radial heat flux of TEM instability decreases due to the zonal flow effect.Figure 10c shows that this zonal flow effect is weaker than the collisionality one.The reduction of radial heat flux is more significant for deuterium plasma (open and closed blue circles) than for hydrogen plasma (open and closed red squares), as expected from Eq. ( 6).It should be noted that the zonal flow effect reverses the isotope mass dependence at the higher collisionality (deuterium radial heat flux is higher than hydrogen radial heat flux without zonal flow but lower with it).At lower collisionality, the zonal flow effect becomes weak.Because of the collisional stabilization effect, the mass dependence of the TEM can be reversed and be opposite to that of the ITG in medium collisionality ( ei = 0.04 ∼ 0.1 in LHD and 0.02 ∼ 0.04 in CBC-tolamak).ITG and TEM instability have gyro-Bohm type ion mass dependence in a low collisionality regime.In contrast, a reversal of mass dependence may occur in a medium collisionality regime, if the TEM is dominant.

Reversal of mass dependence
In cases of plasma with relatively flat density profiles, ITG instability becomes dominant in the core and TEM instability becomes dominant near the plasma edge.When the collisionality of the region where the TEM becomes unstable is medium range, the reversal of mass dependence may between core and edge.Figure 11a shows radial profiles of total energy flux ( Q e + Q D ) comparing CGYRO turbulence simulations with an experimental DIII-D power balance (Belli et al. 2017).The ITG instability is dominant in the core region and TEM instability is dominant near the plasma periphery.The rapid increase at r/a = 0.9 (note the log scale) is driven by non-adiabatic electron physics and is highly sensitive to the electron-to-ion mass ratio, and also to the safety factor q.
Figure 11b shows nonlinear ion energy flux normalized by deuterium gyro-Bohm flux, Q GBD , for hydrogen (H), deuterium (D), and 50:50 hydrogen and deuterium (DT) plasmas.In the ITG-dominated regime (core plasma), the fluxes have negligible mass dependence as , suggesting that the naive gyro-Bohm scaling is broken.In the TEM-dominated regime (plasma periphery), a significant reversal from the naive scaling is found as Q i (H) >> Q i (D) >> Q i (DT) .These char- acteristics are qualitatively consistent with the difference in a normalized growth rate between ITG and TEM instability, where R ax ∕v ts (H) ∼ R ax ∕v ts (D) ∼ R ax ∕v ts (T) for ITG instability and R ax ∕v ts (H) > R ax ∕v ts (D) > R ax ∕v ts (T) for TEM instabil- ity as seen in Fig. 9c, d.This shows that the radial energy flux of deuterium plasma is lower than that of hydrogen plasma near the plasma periphery, where the TEM instability is dominant.The radial energy flux of DT plasma is significantly reduced in this region.The reversal of the isotope mass effect plotted in this figure is due to the non-adiabatic correction (finite m e ∕m i correction).Better confinement for larger isotope mass in the TEM dominant regime indicated here is consistent with the reversed ion mass dependence (opposite to gyro-Bohm type mass dependence) plotted in Fig. 10.

Particle transport
The isotope effect on particle transport is observed in tokamak and helical plasma.The density gradient determined by the particle transport influences the stability of ITG and TEM instability.The sharp density gradient contributes to the stabilization of ITG instability but tends to destabilize the TEM instability.Therefore, the secondary effect on thermal transport through the density gradient varies depending on the type of instability.Figure 12a, b shows radial profiles determined by sinusoidal gas modulation in the hydrogen and deuterium plasma with hydrogen neutral beam injection (NBI) in ASDEX (Bessenrodt-Weberpals et al. 1993).The diffusion coefficient and pinch velocity were studied in a wide range of heating power (from 0.6 to 1.4 MW).The experimental results show that the particle transport coefficient is insensitive to plasma temperature and collisionality.The diffusion coefficient for deuterium plasma is lower than that for hydrogen plasma by a factor of two.The L mode of high density, NBI heated plasmas ( P NBI ≤1.4 MW), shows a scaling D ∝ M −1 similar to that of the Ohmic case.Quantitatively, the mass dependence of the diffusion coefficient is weak D ∝ M −1∕2 for low density ( n e = 3 × 10 19 m −3 ) and becomes stronger D ∝ M −1 at higher density ( n e = 5 × 10 19 m −3 ).The diffusion coefficient increases as the power of hydrogen neutral beam injection is increased.The inward convection (pinch velocity) is larger for deuterium than for hydrogen.The observations of different transport coefficients agree well with the finding that the particle confinement for deuterium is superior to that for hydrogen.A similar experiment was performed in CHS helical plasma.The density dependence of D mod and V mod are evaluated from the density modulation phase and the amplitude with gas puff modulation experiment, as seen in Fig. 12c, d (Tanaka et al. 2016).The horizontal error bars indicate the density regime of the analysis time window and vertical error bars indicate the error of the analysis.At a higher density, above 2.5 × 10 19 m −3 , there is no difference of diffusion coefficient between hydro- gen and deuterium dominant plasma.However, the diffusion coefficient is smaller for deuterium plasma than that for hydrogen plasma at low density, below 2.5 × 10 19 m −3 .The convection velocity at = 0.6 is inward convection (pinch velocity) except for the very low density in the hydrogen plasma.The magnitude (absolute value) of inward velocity is larger for deuterium.Although the better particle confinement of deuterium plasma than hydrogen plasma is consistent with the observation in ASDEX, there is some difference in density dependence.The mass dependence becomes stronger for lower density in the CHS, but for higher density in ASDEX.The magnetic shear is negative in CHS, while the magnetic shear is positive in ASDEX.This sign of differences of magnetic shear would be one of the candidates for explaining the disparity between these two devices.In JET-ILW H-mode, the density limit exhibits a dependence on the isotope mass (Huber et al. 2017).The density limit is up to 35% lower in hydrogen, compared to similar deuterium plasma conditions.The density limit is determined by the edge density rather than the core density.Since the pinch velocity results in a peaked density profile with low edge density, deuterium plasma which has pinch velocity, is expected to have a larger line-averaged density and a higher density limit.

Impurity transport
The isotope mass has a significant impact on impurity transport as a primary effect, and the impurity density and its gradient affect thermal transport as a secondary effect.(Osakabe et al. 2014;Ida et al. 2019).Figure 13a-c shows the time evolution of line-averaged electron density, the ratio of central carbon density to that at the ITB foot, and the central ion temperature, C p , for a discharge with ion transport bar- rier (ITB) formation, triggered by a carbon impurity injection for hydrogen (H) and deuterium (D) plasma in the LHD (Ida et al. 2019).The transport barrier appears only in the ion heat transport, not electron heat transport.The central electron temperature is only 3 keV and unchanged after the carbon pellet injection.There is no difference in electron temperature profiles between hydrogen and deuterium plasmas.Here, the ratio above unity represents a peaked ( dn c ∕dr eff < 0 ) carbon density profile and that below it represents a hollow ( dn c ∕dr eff > 0 ) one.Before carbon pel- let injection, the carbon density profile is slightly hollow.After the carbon pellet injection, it becomes transiently peaked for deuterium plasma, while it becomes more hollow for hydrogen plasma.Plasma with a very hollow carbon density profile is called an impurity hole.When the carbon density profile stays hollow, the increase of central ion temperature is transient and starts to decrease quickly, due to transport degradation.
The radial profiles of ion thermal diffusivity are evaluated for hydrogen plasma with an impurity hole ( C p = 0.4) and deuterium plasma with a peaked carbon density profile ( C p = 1.4).The ion thermal diffusivity sharply increases towards the magnetic axis for the hydrogen plasma, while it stays low for deuterium plasma.The sharp increase of ion thermal diffusivity is due to the formation of the impurity hole where the carbon density gradient is positive ( dn c ∕dr eff > 0 ).The ion thermal diffusivity near the magnetic axis ( r eff ∕a 99 = 0.2 ) is plotted as a function of a normalized carbon density gradient of R∕L n,c .Here, the normalized carbon density gradient is defined as R∕L n,c = −R(dn c ∕dr eff )∕n c .Although the impurity hole appears both in hydrogen and deuterium plasma, the formation of such holes is much faster in hydrogen plasma, as seen in Fig. 13a-c.Figure 13d shows the thermal diffusivity profile after the impurity hole formation for hydrogen, but before that for deuterium plasma.Figure 13e shows thermal diffusivity near the plasma center, including up to the end of the impurity hole formation at t = 5.17 s for hydrogen and deuterium plasma.A significant increase of ion thermal diffusivity is observed, associated with the formation of the impurity hole ( R∕L n,c < −5 ) both for hydrogen and deuterium plasma.Therefore, the difference in the thermal ion transport between hydrogen and deuterium plasma is attributed to the difference in carbon impurity density and its gradient and is considered to be a secondary isotope effect through the difference in impurity transport.
The impacts of impurity concentration and density gradient on thermal diffusivity are studied in theory and simulation.Figure 14a, b shows the normalized growth rate and mode frequency as a function of L ez for a different concentration, f c , (Guo et al. 2016).Here, L ez is defined as L ez = L n e / L n z , and L n e and L n z is the scale length of the electron density gradient and impurity density gradient.The normalized growth rate decreases as the L ez increases to a positive value, in which case the impurity density profile is more peaked than the electron density profile.In contrast, the normalized growth rate increases for negative L ez , where the impurity gradient is opposite to that of the electron density.This is a case where the impurity density profile is hollow while the electron one is peaked.The influence of the density gradient becomes strong for a higher impurity concentration of 3% ( f c = 0.03).The absolute value of the mode frequency decreases as the L ez is increased.
The influence of impurity concentration and gradient on thermal transport is also studied using the GENE simulation code in a flux-tube approximation and input parameters from the JET discharge.As seen in Fig. 14c, the ion heat flux normalized by gyro-Bohm (gB) units starts to increase above the critical normalized ion temperature gradient of R∕L Ti (Bonanomi et al. 2018).The ion heat flux in the plasma with an impurity ( Z eff = 3) is significantly larger than in that without impurity ( Z eff = 1) due to turbulence reduction by the impurity.It is interesting that the critical normalized ion temperature gradient is sensitive to the local gradient of nitrogen impurity density, R∕L n,N , even for the same concentration of Z eff = 3.The critical value is 2.5 for the hollow profile ( R∕L n,N = -1) and increases to 4.2 for the peaked one ( R∕L n,N = 1.4), and 5 for one that is more peaked ( R∕L n,N = 2.8).Because of the increase of critical value, the ion heat flux becomes lower at the given normalized ion temperature gradient of R∕L Ti as the impurity profile becomes more peaked.
These theoretical predictions and simulation results are consistent with experimental observation in the LHD.The stabilizing effect of heavier impurity has also been pointed out by the gyro-kinetic analysis for Argon seeded H-mode plasma in JT-60U (Urano et al. 2015).The gyro-kinetic analysis shows that the linear growth rate and quasi-linear heat flux normalized by the potential fluctuations evaluated with the GKV code at the mid-radius (r/a = 0.5) decreases by a factor of two as the fraction of Argon concentration increases from 0 to 0.8 % ( Z eff from 2.4 to 4.9) The reduction of the growth rate and quasi-linear heat flux is due to ion dilution and increasing Z eff with the ITG-TEM mode.The linear growth rate is also investi- gated with the GKV code for plasma with Argon impurity for ITG and ETG modes (Nakata 2022).The stabilizing effect of heavier impurity is more significant for the ETG mode.
In an experiment, the isotope effect of thermal transport is weak, but that of impurity transport is strong, as seen in the LHD experiment (Ida et al. 2019).The isotope effect in impurity transport was characterized by a smaller diffusion coefficient and smaller outward convection for heavier isotope ions and deuterium in the LHD experiment (Mukai et al. 2018).In the simulation, GKV was applied to the burning plasma with a mixture of deuterium, tritium and helium ash.Although the isotope effect was weak in the heat transport, a relatively strong isotope effect was seen in the particle flux.The radial particle of heavier ions, tritium in this simulation, is predicted to be much lower than that of deuterium with the existence of the helium ash (Nakata and Honda 2022).

Zonal flow
Zonal flows are azimuthally symmetric band-like shear flows, driven by drift wave turbulence (Fujisawa 2009).This was experimentally identified by the coherence of plasma potentials measured with two heavy ion beam probes (HIBP) in the Compact Helical System (CHS) (Fujisawa et al. 2004).Anti-correlation between the observed fluctuation amplitude and zonal flow amplitude is explained by the predator-prey model between the zonal flow and drift wave turbulence (Diamond et al. 1994;Kim and Diamond 2003;Diamond et al. 2011).
The properties of local turbulence and long-range correlations (LRC) were investigated in hydrogen and deuterium plasmas in the TEXTOR tokamak.Long-range correlations (LRC) are evidence of zonal flows, because a long-distance cross-correlation of potential fluctuations along the same flux surface is expected for zonal flows.Figure 15a plots the amplitude of the long-range correlation in floating potential signals C xy ( = 0) versus an H concentration for the plasma with four different magnetic fields of B T = 2.6T (green), 2.25T (blue), 1.9T (red), and 1.6T (yellow), plasma current I p = 250-400 kA, and electron density of 2.0-2.5 × 10 19 m −3 (Xu  2016).For each pair of B T , the D-dominated plasmas have relatively higher LRC values than H-dominated ones.This result shows a systematic increase in the amplitude of long-range correlations during the transition from hydrogen to deuteriumdominated plasmas, regardless of plasma parameters.
A similar result was obtained in the Heliotron-J experiment.The ratio of zonal flow amplitude (< 4 kHz) to turbulence amplitude (10-45 kHz) is plotted in Fig. 15b (Ohshima et al. 2021).The zonal flow amplitude is enhanced relative to turbulence amplitude in deuterium discharges, and zonal flow activity is more dominated in D plasmas, which is consistent with the isotope ratio dependence of LRC values in TEXTOR.The enhanced zonal flow is one of the candidates for causing the reduction of transport in deuterium plasma.The isotope effect on zonal flow has been investigated theoretically (Hahm et al. 2013) and with numerical simulations using the gyrokinetic electromagnetic numerical experiment (GENE) code (Jenko et al. 2000).The zonal flows can play an important role in the saturation mechanisms of nonlinear simulations.Figure 16a shows the zonal flow time trace at a spatial scale in which isotopic dependence of the residual level of zonal flows is present (Bustos et al. 2015).The residual level of the zonal flow of deuterium (D) plasma is larger than that of hydrogen (H) plasma by 30%.The residual level of zonal flow for tritium (T) plasma is larger than for deuterium (D).The nonlinear GKV simulation has shown the enhancement of zonal flow amplitude normalized by the turbulence amplitude for hydrogen and deuterium plasmas in the LHD (Nagaoka et al. 2019;Nakata et al. 2019).
It is well known that E × B flow shear can suppress the turbulence, but the mean E × B flow itself has no direct impact on turbulence suppression.However, the mean E × B flow is expected to enhance the zonal flow in helical plasma.The effect of a radial electric field ( E × B flow) on zonal flow and turbulence was investigated for ITG instability in an LHD-type configuration using the GKV code.Although the zonal flow damping is larger in helical than tokamak plasma (Xu 2016), the radial electric field appears in helical plasma, reducing zonal flow damping and enhancing zonal flow amplitude.This process plays an essential role in forming internal transport barriers in helical plasma, where the zonal flow damping is larger than in a tokamak (Itoh et al. 2007).Figure 16b shows the ratio of the zonal flow amplitude, Z, and the turbulent fluctuation amplitude, T, with different poloidal Mach numbers, M p = 0 and 0.3 (Watanabe et al. 2011).The zonal flow amplitude normalized by the turbulent fluctuations, Z/T, increases after the saturation of the instability growth at t ∼ 40L n ∕v ti in a case with the large poloidal Mach number of M p = 0.3.The Z/T values for M p = 0.3 reaches to 1.5 times of that without poloidal flow ( M p = 0).These simulation results suggest that the zonal flow response enhancement due to the mean E × B flow plays a positive role in turbulence suppression and trans- port reduction.The mean E × B flow shear has a direct isotope effect on transport, as indicated in Eq. ( 6) in Sect.4.1.The simulation suggests the importance of the indirect effect of mean E × B flow shear on transport through modification of the residual level of zonal flows.

Transition power threshold
The isotope effect on heating power required for the transition from low confinement (L-mode) to high confinement mode (H-mode) has been studied in various tokamaks.The lower transition power threshold observed is qualitatively consistent with the prediction of the H-mode model based on parallel viscosity (Shaing and Crume 1989;Rozhansky 2004).These models predict that the L-to-H-mode transition occurs when the poloidal Mach number [ = U B∕(v ts B ) , where U is poloi- dal velocity due to E × B drift] exceeds the critical value of ∼ 1.Then, the poloi- dal velocity required for the L-mode to H-mode transition is smaller in the plasma with heavier isotope mass for the same radial electric field.The heating power to access the H-mode, P LH , scales approximately inversely with the isotope mass of the main ion plasma species in mixed hydrogen-tritium and pure tritium plasmas at JET with an ITER-like wall (Birkenmeier et al. 2022).A comprehensive set of L-H transition experiments has been performed, and a significant impact of helium on threshold power for L-H transition has been found in DIII-D and NSTX.The threshold power starts to increase when helium concentration levels in deuterium plasmas exceed 40% and reach a level twice the threshold power of deuterium plasma in pure helium plasma (Gohil et al. 2011).In NSTX, the impact of helium is weaker, and the L-H power threshold is approximately 20-40% greater in helium than in deuterium (Kaye et al. 2011).
Since the isotope effect appears much more clearly as a difference in power threshold to the transition to an improved mode such as the H-mode and the internal transport barrier (ITB), the power threshold has been intensively studied in various experiments.The isotope effect on L-H threshold power for an L to H-mode transition, P L−−H , is investigated in the JET-ITER-like Wall (JET-ILW) experiment in hydrogen and deuterium plasmas with ICRH heating, as seen in Fig. 17a  ).The isotope effect is more significant, especially in a low-density regime.The threshold power, P L−−H , for the deuterium plasma is one-third of that for the hydrogen plasma at a low density of 2 × 10 19 m −3 .As the density increases, the reduction of P L−−H for the deuterium plasma becomes less significant (half that of the hydrogen plasma).The threshold power, P L−−H , for a 50:50 H-D mixture plasma is always in between P L−−H for the deuterium plasma and P L−−H for the hydrogen plasma.However, there is no linear relation between the isotope ratio and threshold power.A similar experiment was done in ASDEX-U, as seen in Fig.
17b (Ryter et al. 2016).The threshold power, P L−−H , in the deuterium plasma is lower than that in the hydrogen plasma by a factor of two, The electron density for deuterium's minimum P L−−H is somewhat lower than that for hydrogen, which is also consistent with the JET results.The edge ion heat flux at the L-H transition, (taken at pol = 0.98), increases linearly with the line-averaged density.The reduction of threshold power for the transition to improved confinement plasma is also observed for plasma with an electron internal transport barrier (ITB) in the LHD. Figure 17c shows the peak-to-peak modulation amplitude of the electron temperature gradient, as a function of the applied ECH power, normalized by line averaged density (Kobayashi et al. 2022).This experiment modulates ECH power in a marginal regime to form an electron-ITB.Therefore, the large modulation amplitude indicates that the plasma repeats the formation and termination of the electron-ITB, synchronized with ECH on-off modulation.The ECH power at a sharp increase of the peak-to-peak modulation amplitude is the threshold power for a transition from L-mode to electron-ITB plasma.The threshold power in deuterium plasma is lower than that in hydrogen plasma, which is consistent with the isotope effect of the threshold power L-H transition in a tokamak.H-D mixed plasma's threshold power is between that in hydrogen and deuterium plasma.However, the reduction of the threshold power in deuterium is only ∼ 30 %, and the isotope effect on threshold power seems relatively weak compared with that in a tokamak.At the heating power marginal to the threshold power for the formation of the electron ITB and ion-ITB, a clear confinement improvement is observed for the deuterium plasma more than for the hydrogen plasma (Kobayashi et al. 2021).
Recently, the isotope effect on transport has been studied in hydrogen and deuterium mixture H-mode plasma with various H-D ratios (so-called effective mass scan), to investigate the linearity of the isotope mass.Figure 18a shows thermal stored energy calculated by TRANSP vs. an effective mass for mixed isotope plasmas (blue), including those with very low deuterium content (green) and pure isotope plasmas (red) in JET (King et al. 2020).The data show the appearance of a complex dependence on isotope ratio.The thermal stored energy is low for the hydrogen plasma with an effective mass of 1 (red points) and high (almost twice that of hydrogen plasma) for deuterium plasma with an effective mass of 2. The thermal stored energy in the pure deuterium plasma is 1.9 times that of hydrogen plasma, which is consistent with Eq. (3), discussed in Sect.2.1.
The thermal stored energy in the mixture plasma is 1.3 times of that of hydrogen plasma.There is no significant confinement dependence on the isotope mixture for an effective mass range from 1.2 to 1.8 (blue points).Because the heating power for these experiments is close to the threshold power for the L-H transition, it is unclear whether the jump of the thermal stored energy of dominant deuterium plasma at an effective mass of 1.8-2.0 is due to the L-H transition or the non-linear isotope effect of global energy confinement.Therefore, it is also interesting to question how the threshold power for the L-H transition depends on the isotope mass.
Figure 18b, c shows the electron density and temperature at the pedestal top ( pol = 0.95) as a function of the effective mass.At a constant gas fueling rate, the D-rich plasma features a higher density pedestal, which is consistent with the higher particle confinement in D-plasma discussed in Sect.5.1.However, the pedestal top temperature has the opposite trend and decreases due to the increase of density, and the pedestal pressure is almost constant in a wide range of effective mass in the mixture plasma, which is also consistent with no significant confinement dependence on the isotope mixture, for an effective mass range from 1.2 to 1.8 in Fig. 18a.Nonlinear behavior is also seen in the power threshold for the L-H transition in EAST, which is clearly seen in Fig. 18d (Shao et al. 2021).The power threshold starts to drop sharply for the hydrogen faction n H ∕(n H + n D ) < 0.15.This result does not agree with the empirical power and fits P L−−H ∕P scale ∼ 2∕A eff with a linear isotope mass A eff dependence (Shao et al. 2021), which is indicated by the magenta dashed line.In the hydrogen fraction n H ∕(n H + n D ) of 0.15-0.45, the mass dependence on the power threshold is very weak.In contrast, at the range of the low hydrogen fraction, n H ∕(n H + n D ) < 0.15 (dominant deuterium plasma), mass dependence on the power threshold for L-H transition is strong.

Isotope mixing
Isotope mixing is one of the key kinds of physics in isotope mixture plasma because control of the isotope ratio is essential to optimize fusion power in deuterium-tritium (D-T) plasma.The isotope mixing is a mechanism different from the conventional diffusion convection model, where the particle flux of ion species s is determined by the diffusion coefficient D s and convection velocity, v s , as Γ s = −D s (dn s ∕dr) + v s n s .In this mode, particle transport is independent of different isotope species.In other words, the hydrogen and deuterium density profiles are determined independently by the source profile of each species and the particle transport with coefficients of ( D H , v H ) and ( D D , v D ), respectively.Isotope mixing is the mechanism causing the blending of the different ion species with the constraint of quasi-neutral conditions.Therefore, when the isotope mixing occurs, the normalized density gradient of each ion species becomes identical to that of the electron as R∕L nH ∼ R∕L nH ∼ R∕L ne , when the concentration of impurity is low.The density profile shape of each species becomes identical, regardless of the source profile of each species.
The isotope mixing occurs when the ion diffusion is larger than the electron diffusion ( D i ≫ D e ).Please note that this diffusion coefficient is a theoretical value ignoring the quasi-neutral conditions in a steady state.(In the steady-state, D i = D e for plasma with one isotope plasma).The nonlinear fixed gradient gyrokinetic simulations by GKW predict D i ≫ D e for plasma where ITG instability is dominant and D e ≫ D i for plasma where TEM instability is dominant.The radial profiles of hydrogen, deuterium, and electron density profiles ( n H , n D , n e ) and electron and ion temperatures ( T e , T i ) are plotted in Fig. 19a, b for the high-and low-density plasmas with T e ≫ T i (Bourdelle et al. 2018).The ITG instability is dominant in the high- density case, while the TEM instability is dominant in the low-density case.In that of high density, the hydrogen density profile is identical to the deuterium one, due to the isotope mixing.In contrast, the deuterium density profile is more peaked than the hydrogen one, due to the difference in the source (deuterium injection to hydrogen plasma).
The isotope density profiles are directly measured by charge exchange spectroscopy in the LHD (Ida et al. 2019).As seen in Fig. 19c, d, there are two different isotope density profiles (two states) for a similar source profile of each isotope species (Ida et al. 2020).Here, the hydrogen density measured with bulk charge exchange spectroscopy contains a thermalized hydrogen beam, but does not include the hydrogen beam component.The beam component has a relatively small fraction, which is supported by the fact that the radial profile on electron density, measured with YAG Thomson scattering, is almost identical to the sum of isotope density measured with bulk charge exchange spectroscopy.In this experiment, the core fueling is by hydrogen beam, while edge fueling is deuterium recycling.At the higher density ( n e = 3.8 × 10 19 m −3 ), the deuterium density profile is identical to the hydrogen one, which exhibits the isotope mixing state.However, at the lower density ( n e = × 10 19 m −3 ), the hydrogen density profile peaks due to core hydrogen beam fueling.In contrast, the deuterium density profile is hollow, due to edge deuterium recycling, which exhibits the isotope non-mixing state, in which ion diffusion is larger than electron diffusion.In this case, the radial profile of ion isotope species becomes identical due to ion mixing.Due to the quasi-neutral condition, the radial profile of electron density also becomes similar to that of the ions.The deeper penetration of deuterium ions is due to the mixing with hydrogen ions, not due to the pinch of deuterium ions.The shape of the radial electron density profile is identical between these two states, which shows that the electron density profile is hard to constrain.The fast transition from the non-mixing state to the isotope-mixing one is observed, associated with the increase of electron density by the pellet injection near the plasma periphery, regardless of the species of pellet.Figure 20a shows the radial profile of the hydrogen faction before and after the deuterium pellet injection (Ida et al. 2020).Here, the deuterium pellet deposits at r eff ∕a 99 = 0.9.The hydrogen fraction profile becomes flat after the deuterium pellet injection.This is other clear evidence of isotope-mixing because the hydrogen fraction profile should be peaked if the isotope-mixing does not occur.The transition from an isotope non-mixing state to an isotope mixing one is accompanied by the transition of the turbulence state, which appears as a change in the turbulence frequency spectrum, as seen in Fig. 20b (Ida et al. 2021).The peak frequency of turbulence is relatively high ( ∼ 80 kHz) in the isotope non-mixing state, while it becomes lower ( ∼ 25 kHz) in the mixing state.The linear growth rate calculated at r eff ∕a 99 = 0.8 with GKV based on the density and electron and ion temperature profile measurements also shows the transition from a TEM unstable state to an ITG unstable one associated with the transition from the isotope non-mixing to the isotope mixing state, as seen in Fig. 20c (Ida et al. 2020).The characteristics of the linear growth rate calculated with the GKV code are consistent with the prediction by the nonlinear simulation code GKW plotted in Fig. 20d (Bourdelle et al. 2018).The ITG instability enhances ion diffusion ( D i ≫ D e ) and causes isotope mixing, while the TEM instability only enhances electron diffusion ( D e ≫ D i ) and does not cause isotope mixing.Complicated particle transport depending on the species has also been revealed by the nonlinear GKV simulations for the D-T-He mixture plasma with ITER-like tokamak geometry (Nakata and Honda 2022), where the optimal balance among the turbulent thermal and particle fluxes for the steady burning is identified.The exhaust of the helium ash produced by the fusion reactions is an essential issue in burning plasma such as ITER and DEMO.Neoclassical theory predicts that helium ash stays to be accumulated in the plasma center due to the collision process between helium ions and bulk ions.Therefore, the turbulence state causing the ion mixing process between bulk ions and helium impurity is preferable for the efficient exhaust of the helium ash in the burning plasma.

Summary
According to the gyro-Bohm model, the isotope effect on thermal diffusivity is expressed as ∝ M 1∕2 , and the heat flux is defined as n dT∕dr) .However, the iso- tope effect on thermal diffusivity has been found not to have a simple power law dependence, but be determined by a combination of complex mechanisms.This is because various parameters affect transport and confinement besides isotope mass.For example, density gradient, dn e ∕dr , and impurity gradient, dn z ∕dr , are key parameters affecting electron and ion thermal diffusivities.E × B flow shear and the zonal flow amplitude significantly impact the suppression of turbulence.In helical plasma, the radial electric field enhances zonal flow amplitude.Therefore, the isotope mass dependence on particle convection, neoclassical transport, Reynolds stress, Residual stress, and growth rate determine the final isotope mass dependence on thermal diffusivity.The direct effect of isotope mass on thermal diffusivity is categorized as the primary effect, while the indirect one is categorized as a secondary isotope effect.In this review paper, secondary isotope effects are discussed as well as primary ones.
Various approaches to comparison studies with different isotope masses are also discussed, depending on the comparison method, such as simple comparison (operational parameters), profile matching comparisons (dimensional and non-dimensional parameters), threshold power for H-mode and ITB formation, and zonal flow amplitude, mass dependence looks different.Although the mass dependence looks weak in a simple comparison, it becomes much more significant in profile matching.The profile matching comparison with non-dimensional parameters clearly demonstrates a break of the gyro-Bohm mass dependence.The comparison of threshold power 23 Page 36 of 42 is the most useful, because its reduction for a large isotope mass is clearly seen in tokamak and helical plasma.After the transition to H-mode, the isotope effect appears in pedestal top pressure (density and temperature), because the pedestal width depends on the ion gyro-radius, and the MHD stability determines the pressure gradient.Therefore, the isotope effect on pedestal top pressure is not an isotope effect through turbulence and transport.The isotope mass dependence of the pedestal is M 0.96 , while the mass support of core confinement is M 0.03 .Since the pedestal top pressure is a boundary condition for core transport, it has a strong impact on the mass dependence of global energy confinement.
Although the isotope effect seems to be weaker in helical plasma than that in a tokamak, there is almost no difference in the isotope mass dependence in the core transport.Because the database for the isotope effect study in the tokamak is mainly ELMy H-mode, the stronger isotope effect in the tokamak is attributed to the higher pedestal top pressure, which has strong mass dependence.One of the candidates to explain the difference between tokamak and helical plasma is MHD stability of the edge pedestal (in fact, in many cases, there is no ELM in helical plasma).Another difference is the mass dependence on the threshold power.The reduction of threshold power to an improved mode seems smaller in helical plasma.The weaker isotope mass effect on zonal flow observed in helical plasma is another candidate to explain the difference between tokamak and helical plasma.
The nonlinearity of the isotope effect is observed in the isotope mixture plasma.The isotope effect in this plasma cannot be interpolated from pure isotope plasma (pure hydrogen, deuterium, and tritium plasma).In other words, mass dependence cannot be expressed with the power law of mass, such as M in the isotope mixture plasma, A power law expression of the mass dependence can indicate the strength of mass dependence in discussing whether it is strong or weak in the comparison between pure isotope plasmas (pure hydrogen, deuterium, tritium plasmas).The isotope mixing is key physics in isotope mixture plasma, because the isotope mixing should be required to optimize fusion power in deuterium (D) and tritium (T) plasma in the future.Although understanding the isotope effect is essential to predict the performance of D-T plasma, utilization of the isotope mixing is critical in controlling the D-T plasma.
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Fig. 5
Fig. 5 Radial profiles of ion thermal diffusivity from TRANSP before and after the L-H transition for DD and DT H-mode discharge in TFTR, DD and DT discharges in JET, and hydrogen and deuterium plasma in JT-60U (from Fig. 4a, b in Bush et al. (1995), Fig. 2 in Cordey et al. (1999), and Fig. 4d in Urano et al. (2012))

Fig. 6 a
Fig. 6 a Maximum pedestal density and temperature (n-T diagram) for five series of gas scans at fixed plasma shape in JET.b ELM frequency as a function of net power crossing the separatrix for the 1.0 MA/1.0 T dataset in JET.c Pedestal top density as a function of f ELM in low (= 0.2) H (red) and D (blue) plasmas at 1.4 MA/1.7 T (full circles) and 1.0 MA/1.0 T (open triangles) in JET.d The pedestal n-T diagram in the cases of hydrogen and deuterium plasmas performed at I p = 1 MA, B T = 2 T and P abs = 8-9 MW in JT-60U.e Dependence of ELM frequency on the power crossing the separatrix P sep at 1.1 MA and 2.4 T ( q 95 = 3.7) in JT-60U.f Dependence of the thermal energy confinement time th on P abs in JT-60U.(from Fig. 26 in Saibene et al. (1999), Figs.1b and 10a in Horvath et al. (2021), Figs.1b, 6 and 7 in Urano et al. (2012))

Fig. 7 a
Fig. 7 a Radial profiles of a ion temperature and b ion thermal diffusivity for the hydrogen and deuterium plasmas in the profile matching experiment in JT-60U and c electron temperature and d electron thermal diffusivity for the hydrogen and deuterium plasmas in the profile matching experiment in the LHD (from Fig. 2a, d in Urano et al. (2012) and Fig. 15c, e in Takahashi et al. (2018))

Fig. 8
Fig. 8 Radial profile of dimensionless effective thermal diffusivity M eff ∕B (m 2 /s/T) for the a ELMy H-mode and b L-mode isotope identity pair in hydrogen (H) and deuterium (D) discharge in JET.Comparison of the c electron and d ion thermal diffusivity in a pair of dimensionlessly similar hydrogen (solid curves) and deuterium (dashed curves) plasmas in the LHD.Thermal diffusivity is normalized by the ion cyclotron frequency.e The ratio of thermal diffusivity in a deuterium plasma to that in a hydrogen plasma at (r eff ∕a) = 2∕3 as a function of the collisionality in LHD plasma.Open and closed circles are the electron heat transport and ion heat transport, respectively (from Fig. 5 in Cordey et al. (2000), Fig. 5 in Maggi et al. (2019), Figs. 3 and 4a in Yamada et al. (2019))

Fig. 9 a
Fig. 9 a Growth rate normalized with the phase speed of electron drift wave for ITG mode, b growth rate for DTE mode, c, d growth rate normalized with ion thermal speed, v ts , of each species, s, for ITG, TEM, and e growth rate normalized with electron thermal speed, v te , for TEM-ETG instability as a function of poloidal wavenumber for different hydrogen isotope species of hydrogen (H), deuterium (D), and tritium (T) (from Fig. 1 in Dong et al. (1994), Fig. 1 in Tokar et al. (2004), and Figs.4a, b, and 5a in Nakata et al. (2016))

Fig. 10 a
Fig. 10 a Collisionality dependence of the radial heat flux with the turbulent diffusivity ∕k 2 ⟂ for the linear TEM (L-TEM) and ITG (L-ITG) instability for hydrogen (H), deuterium (D), and tritium (T) plasmas in the LHD inward shifted configuration, where k x ts = 0, k y ts = 0.4 and s = (H, D, T).Collisionality dependence of the radial heat flux for b ITG and c TEM instability in CBC-like tokamak plasmas, where the linear mixing length (L) is plotted by dashed lines and the corresponding nonlinear (NL) results are plotted with symbols (from Figs. 1 and 4 in Nakata et al. (2017))

Fig. 11 (
Fig. 11 (Radial profiles of a total energy flux ( Q e + Q D ) comparing CGYRO turbulence simulations with experimental DIII-D power balance and b nonlinear ion energy flux, normalized by deuterium gyro-Bohm flux for hydrogen (H), deuterium (D), and 50:50 hydrogen and deuterium (DT) plasmas (from Figs. 1 and 2 in Belli et al. (2017))

Fig. 12
Fig. 12 Radial profiles of a diffusion coefficient and b pinch velocity (inward velocity) in hydrogen (H) discharge ( I p = 320 kA, B T = 2.2 T , n e = 3 × 10 19 m −3 ) and deuterium (D) discharge ( I p = 380 kA, B T = 2.2 T, n e = 4.4 × 10 19 m −3 ), with hydrogen beam injection power of 0.6, 0.9, 1.4 MW. c Diffusion coefficient and d convection velocity at normalized minor radius of =0.6 as a function of line averaged electron density in the CHS beam heated plasma.Red circles stand for diffusion and convection velocity for hydrogen plasma, while blue squares stand for that of deuterium plasma.Here, the negative convection velocity is inward and positive velocity is outward (from Figs. 4a and 20a, b in Bessenrodt-Weberpals et al. (1993) and Fig. 8a,b in Tanaka et al. (2016))

Fig. 13
Fig. 13 Time evolution of a line-averaged electron density, b ratio of central carbon density to the carbon density at the ITB foot and c central ion temperature.d Radial profile of ion thermal diffusivity in the deuterium (D) plasma with a peaked carbon density profile ( C p = 1.4) and hydrogen (H) plasma with a hollow one ( C p = 0.4).e Ion thermal diffusivity near the magnetic axis ( r eff ∕a 99 = 0.2 ) as a function of a normalized carbon density gradient of R∕L n,c for hydrogen (H) and deuterium (D) plasma (from Figs. 2, 3b and 4 in Ida et al. (2019))

Fig. 14 a
Fig. 14 a Normalized growth rate and b mode frequency as a function of L ez with different impurity concentrations.c Normalized ion heat flux q i,gB from non-linear gyro-kinetic simulation as a function of normalized ion temperature gradient, R∕L Ti without impurity ( Z eff = 1) and with nitrogen impurity with level of Z eff = 3 and for different gradient of nitrogen impurity, R∕L n,N = −1 (hollow), 0 (flat) 1.4 (peaked), 2.8 (more peaked) (from Fig. 1a, b in Guo et al. (2016) and Fig. 3b in Bonanomi et al. (2018))

Fig. 15 aFig. 16 a
Fig. 15 a Amplitude of the long-range correlation in floating potential signals as a function of H concentration.The error bars on C xy ( = 0) indicate the standard deviation about the mean, measured in similar discharges in TEXTOR.b Isotope dependence of the zonal flow amplitude (< 4 kHz) against turbulence amplitude (10-45 kHz) in Heliotron J (from Fig. 2 in Xu (2016) and Fig. 4c in Ohshima et al. (2021))

Fig. 17 a
Fig. 17 a L-H transition power threshold in JET-ILW hydrogen (red stars), deuterium (black up-triangles) and 50:50 H-D mixture (blue down-triangles), with ICRH heating only at 1.8 T/1.7 MA. b P L−−H and Q i,edge (at pol ∼ 0.98) at the L-H transition versus line-averaged density in hydrogen and deuterium.All discharges at 1 MA, B T ∼ 2.5 T. c The peak-to-peak modulation amplitude of the electron temperature gradient as a function of the applied ECH power normalized by the line averaged density.d Deuterium content dependence of the threshold value of ECH power normalized by the line averaged density for the ITB transition (from Fig. 11 in Maggi et al. (2018), Fig. 8 in Ryter et al. (2016), and Figs.1c and 2 in Kobayashi et al. (2022))

Fig. 18 a
Fig. 18 a Thermal stored energy calculated by TRANSP as a function of effective mass for pure hydrogen and deuterium H-mode plasmas (red) and mixed isotope plasmas (blue) in JET.The data indicated by green circles stand for the plasmas with very low deuterium content.Electron b density and c temperature at the pedestal top ( pol = 0.95) as a function of the effective mass.d The threshold power for the L-H transition normalized by scaling, P L−−H ∕P scale , as a function of hydrogen fraction, n H ∕(n H + n D ) , over a hydrogen concentration of 3-45% in EAST (from Figs. 5 and 7 in King et al. (2020) and Fig. 8 in Shao et al. (2021))

Fig. 19 a
Fig. 19 a The final relaxed density profiles are shown in the central panel, and the final temperature profiles are shown in the right panel at 16 s.b Relaxed density (central panel) and temperature (right panel) profiles at 16 s in a TEM-dominated regime.Radial profiles of H and D density in the plasma with H-beam fueling for the different line-averaged density and wall recycling isotope ratio of c 3.8 × 10 19 m −3 ( Γ H ∕Γ D = 0.8), and d 1.9 × 10 19 m −3 ( Γ H ∕Γ D = 0.8 = 0.3) (from Figs. 18 and 21 in Bourdelle et al. (2018) and Fig. 1b, d in Ida et al. (2020))

Fig. 20 a
Fig. 20 a Radial profiles of the hydrogen isotope fraction before and after the deuterium pellet injection, b Density fluctuation spectrum in the isotope mixing and non-mixing states in the hydrogen and deuterium mixture plasma with hydrogen beam fueling.c The linear growth rate at r eff ∕a 99 = 0.8 for the nonmixing and isotope-mixing states calculated with GKV.d Ratios of D i ∕D e and D e ∕D i for a range of input frequencies.The right panel shows the breakdown of the contribution to the diffusivities according to trapped and passing ions, and trapped and passing electrons.Note that the passing electron contribution is always negligible (from Fig. 4b in Ida et al. (2020), Fig. 2a in Ida et al. (2021) and Fig. 6c in Ida et al. (2020) and Fig. 2 in Bourdelle et al. (2018))