Predictive Fokker–Planck Modelling of Confined and Lost Fusion Alpha Particles in ITER

The paper represents results of predictive 3D Fokker–Planck modelling of phase space distributions of fusion alpha particles for basic ITER scenarios (Polevoi et al. in J Plasma Fusion Res Ser 5:82, 2002). We simulate the poloidal profiles of alpha induced current as well as of the fusion power deposition to bulk plasma electrons. It is demonstrated that anisotropy of velocity distributions of alphas results in a rather strong alpha driven current that makes up about 10–15 % of the equilibrium plasma current density in the 4th ITER scenario. We investigate the impact of the alpha driven current on the ITER magnetic configuration. In the 4th scenario fusion alphas are shown to result in *15 % enhancement of the rotational transform and in *11 % enlargement of the Shafranov shift of magnetic flux surfaces. Also we evaluate the capability of gamma diagnostics of high-energy alphas in ITER and examine the collisional losses of fusion alpha particles.


INTRODUCTION
In comparison to the effect of charged fusion products (CFPs) in current tokamaks, CFPs in ITER are expected, due to the significantly enhanced fusion power, to have a stronger impact both on the plasma as well as on the first wall. Therefore development of plasma scenarios and research programs for ITER [2] requires a detailed modelling of fusion-born alphas confined in plasma as well as those lost to the first wall. Here we present results of predictive 3D Fokker-Planck modelling of fusion alphas for ITER Scenario 2 (standard H-mode, I/B = 15MA/5.3T) and for Scenario 4 (steady-state, I/B = 9MA/5.3T) [1].
The main attention is paid to the peculiarities of the velocity and poloidal distributions, f α (v ll , v, R, Z), of confined alpha particles with energies exceeding hundreds of keV. Using the distribution function f α we calculate the poloidal profiles of alpha induced bootstrap current, j α , as well as of the fusion power deposition to electrons, P αe , and ions, P αi . The quantities j α , P αe and P αi characterize the CFPs effect on the plasma equilibrium and on the bulk plasma parameters depending on operation scenarios. To examine the capabilities of diagnostics of confined fast alpha-particles in ITER we evaluate also the R,Z profiles of gamma-emission induced as a result of nuclear interactions of fusion alphas with Be and C impurity ions.
Finally we consider the diffusive loss of fusion alpha particles induced by Coulomb collisions and magnetic field inhomogeneity. We calculate the energy spectra and poloidal distributions of lost alphas as well as the maximum wall load induced by collisional loss of fusion alphas for basic ITER scenarios.

MODELLING RESULTS
The simulation carried out is based on the 3D in constants-of-motion space Fokker-Planck approach previously used for modeling CFPs in TFTR [3][4][5][6] and JET [7,8] as well as for NBI ions in JET [9,10] and ITER [11]. Here we present the results of predictive modeling for fusion alphas in Scenario 2 (standard H-mode) and in Scenario 4 (steady-state operation). For these scenarios Fig.1 displays the mid-plane profiles of safety factor in addition to the critical energy, E cr , Spitzer slowing-down time, τ se of alphas [12], DT fusion rate as well as of Z eff . It is seen both effect of the radial width of alpha particle orbits as well as effect of Coulomb collisions are stronger for the Scenario 4. Note that rather high (>20keV), as compared to present day tokamaks, electron temperature in the ITER plasma core results in relatively high critical energy, E cr ~ 0.9 MeV (see Fig. 1b). As a result, in ITER plasma, collisions with the bulk plasma ions are essential even for partly thermalized alphas with E ~ 1MeV, while in plasmas of present-day tokamaks the alpha-bulk ions collisions affect only the distribution function of well thermalized alphas with E<<1MeV. Correspondingly the collisional loss of fusion alphas, which is predominantly induced by pitch-angle scattering on bulk plasma ions, should be more significant in ITER than in present-day tokamaks.
Note that our modelling supposes an MHD quiescent plasma, and correspondingly we neglect the effect of MHD induced transport of fast ions on the alpha particle confinement. Note in this context, that in ITER one may expect a weaker MHD impact on fast-ion transport than in present-day tokamaks. Reasons for that are, at least in case of MHD turbulence, the reduction of the r * -parameter in ITER plasmas (r * = c s /(w c a) with c s denoting the sound speed, w c the ion gyro-frequency and a the plasma radius), as well as the control of MHD instabilities and potential suppression of turbulence by fusion alphas in ITER (see recent simulation studies in the frame of the FOM programme: http:// www.fom.nl/live/english/about/annual_reports/artikel.pag?objectnumber=257830) .

DISTRIBUTION FUNCTION
Obviously in ITER one may expect noticeable effect of collisional transport on the distribution function of even partly thermalized alphas. This is confirmed by Fig.2 where compared are the contours of the modelled distribution function, f a (R, v ll /v), of fusion alphas with energy E = 3.5MeV and E = 1.89MeV in the plasma mid-plane for both scenarios. It should be pointed out that the source term of fusion alphas is supposed to be mono-energetic. As expected the initial distribution of alphas in the reversed shear plasma (Scenario 4) is broader in R coordinate and is more anisotropic in longitudinal velocity as compared to those in standard 2 nd Scenario. The anisotropy of alpha distributions is clearly seen in Figs. 2a, 2b where co-going 3.5MeV alphas are seen to be shifted to the low-B side as compared to the counter-going ones shifted to the high-B side. Moreover this shift is more pronounced in the case of 4 th Scenario. Evidently the above-mentioned peculiarities of R, v ll /v distributions are in correspondence with the orbit topology of fusion alphas produced in the plasma core. This is demonstrated by Fig.3 where shown are 5 orbits of 3.5MeV alphas born at the magnetic axis (R ax = 6.7m, Z ax = 0.52m) of Scenario 4 plasma with an isotropic pitch-angle 89MeV. The Coulomb collisions induced transport seen to redistribute the fast alphas both in the radial coordinate R as well as in the longitudinal energy. However, the thermalized alphas are still substantially anisotropic over v ll and localised in the core of plasma.

ALPHA-DRIVEN CURRENT
Due to anisotropy in longitudinal velocity the fusion alphas can generate a substantial longitudinal current j α in the plasma. Fig. 4 displays the R, Z distribution of the density of thecurrent driven by fusion alphas in ITER plasmas for 2 nd (LHS) and 4 th (RHS) Scenarios.
Due to the excess of the co-going alphas in the low-B side and of the counter-going ones in the high-B side (see Fig.3) the current j α is identically directed with respect to the equilibrium plasma current in the vicinity of the outer part of mid-plane and is oppositely directed with respect to the equilibrium plasma current near the inner mid-plane of plasma (see also [13,14]). Note that the total alpha driven current j a tot , including that of alphas, j a , and also the electron reversed current, j e , [15] can be represented as where G represents the trapped electron correction to the Ohkawa current [16], Z eff is the effective charge number (see Fig. 1d) and <…> FS means the flux surface average (see Eq. (A12) of Appendix).
Using here expression for G obtained in Ref. [17] we arrive at (1.2) where x = η t /(1-η t ) and η t ~ (r/R) 1/2 stands for the fraction of trapped electrons on the flux surface with radius r. Using the analytical model of tokamak magnetic field with noncircular flux surfaces [18] for η t, applicable for ITER magnetic configuration, we obtain (see Eq. (A11)) where R min is the minimum R along the orbit. respect to the equilibrium plasma current near the inner mid-plane of plasma (see also [13,14]). Note that the total alpha driven current j  tot , including that of alphas, j  , and also the electron reversed current, j e , [15] can be represented as where G represents the trapped electron correction to the Ohkawa current [16], Z eff is the effective charge number (see Fig. 1d) and <…> FS means the flux surface average (see Eq. (A12) of Appendix) . Using here expression for G obtained in Ref. [17] we arrive at       and η t ~ (r/R) 1/2 stands for the fraction of trapped electrons on the flux surface with radius r. Using the analytical model of tokamak magnetic field with noncircular flux surfaces [18] for η t, applicable for ITER magnetic configuration, we obtain (see Eq. (A11))   where R min is the minimum R along the orbit. Fig. 5 displays the midplane profiles of the nd th

Alpha-driven current
Due to anisotropy in longitudinal velocity the fusion alphas can generate a substantial longitudinal current j α in the plasma. Fig. 4 displays the R, Z distribution of the density of the current driven by fusion alphas in ITER plasmas for 2 nd (LHS) and 4 th (RHS) Scenarios. Due to the excess of the co-going alphas in the low-B side and of the counter-going ones in the high-B side (see Fig. 3) the current j α is identically directed with respect to the equilibrium plasma current in the vicinity of the outer part of mid-plane and is oppositely directed with respect to the equilibrium plasma current near the inner mid-plane of plasma (see also [13,14]). Note that the total alpha driven current j  tot , including that of alphas, j  , and also the electron reversed current, j e , [15] can be represented as where G represents the trapped electron correction to the Ohkawa current [16], Z eff is the effective charge number (see Fig. 1d) and <…> FS means the flux surface average (see Eq. (A12) of Appendix) . Using here expression for G obtained in Ref. [17] we arrive at       and η t ~ (r/R) 1/2 stands for the fraction of trapped electrons on the flux surface with radius r. Using the analytical model of tokamak magnetic field with noncircular flux surfaces [18] for η t, applicable for ITER magnetic configuration, we obtain (see Eq.
where R min is the minimum R along the orbit. Fig. 5 displays the midplane profiles of the modelled currents of j α , j e and j α tot for the 2 nd and 4 th ITER scenarios. It is seen that electron

Alpha-driven current
Due to anisotropy in longitudinal velocity the fusion alphas can generate a substantial longitudinal current j α in the plasma. Fig. 4 displays the R, Z distribution of the density of the current driven by fusion alphas in ITER plasmas for 2 nd (LHS) and 4 th (RHS) Scenarios. Due to the excess of the co-going alphas in the low-B side and of the counter-going ones in the high-B side (see Fig. 3) the current j α is identically directed with respect to the equilibrium plasma current in the vicinity of the outer part of mid-plane and is oppositely directed with respect to the equilibrium plasma current near the inner mid-plane of plasma (see also [13,14]). Note that the total alpha driven current j  tot , including that of alphas, j  , and also the electron reversed current, j e , [15] can be represented as where G represents the trapped electron correction to the Ohkawa current [16], Z eff is the effective charge number (see Fig. 1d) and <…> FS means the flux surface average (see Eq. (A12) of Appendix) . Using here expression for G obtained in Ref. [17] we arrive at       and η t ~ (r/R) 1/2 stands for the fraction of trapped electrons on the flux surface with radius r. Using the analytical model of tokamak magnetic field with noncircular flux surfaces [18] for η t, applicable for ITER magnetic configuration, we obtain (see Eq. where R min is the minimum R along the orbit. Fig. 5 displays the midplane profiles of the modelled currents of j α , j e and j α tot for the 2 nd and 4 th ITER scenarios. It is seen that electron 4 predominantly suppresses the poloidally symmetric component of j α and makes the resultant profile of j α tot close to completely asymmetric one in poloidal angle with <j α tot > FS much smaller then <j α > FS and correspondingly with max │j α tot (R<R ax ) │≈ max │j α tot (R>R ax )│. It is important that alpha driven current in 4 th Scenario is about two times higher as compared to those in 2nd Scenario.
From the point of view of the alpha effect on the plasma equilibrium, important is the ratio of the alpha driven current j α tot with respect to the total plasma current j eq [1] neglecting the fusion alpha contribution. Figure 6 compares the densities of j α tot (R<R ax ), j eq (R<Z ax ) and of the total plasma current including fusion alpha contribution (solid black lines) in the plasma mid-plane for 2 nd and 4 th Scenario. It is seen that alpha driven current can comprise a significant part of plasma current and in the case of 4 th Scenario can make up to 10-15% of the equilibrium plasma current density without j α tot as calculated by ASTRA [1]. Therefore alpha current can noticeably affect the plasma equilibrium especially in the case of reversed shear plasma in 4 th Scenario. Note that reversed shear induced enhancement of alpha driven current in ITER is in agreement with the current hole enlargement of j α observed in Monte-Carlo modelling of paper [13]. Important from the point of view of the alpha impact on tokamak plasma is the value of total alpha driven current, I α tot = I α + I e , where (1.4) Table 1 represents the calculated values of current induced by alphas, I α , reversed electron current, I e , as well as total alpha driven current, I α tot , for 2 nd and 4 th Scenario. As expected, electrons compensate substantial part of the alpha induced current (~ 0.7MA in 2 nd scenario and 1.2MA in 4 th scenario). As a result the total current driven by fusion alphas is rather low contributing to full toroidal current only < 0.2MA and < 0.5MA in 2 nd and 4 th scenarios respectively. Evidently the alpha driven current will result in small reduction of safety factor ~ I α tot /I, which amounts ~ 5% in 4 th scenario and only ~ 1% in 2 nd scenario.

PLASMA PARAMETERS
In spite of the rather low effect of total current driven by fusion alphas, j α may result in a consequential redistribution of the toroidal current in the plasma core and thereby alter the plasma equilibrium in addition to I α tot induced enhancement of rotational transform (reduction of safety factor). To demonstrate this we use the code HELENA [19] to evaluate the alpha current effect on the safety factor and the Shafranov shift. Note that with reasonable accuracy the current density j α tot (R,Z) can be approximated by the equilibrium-like profile It is important that alpha driven current in 4 th Scenario is about two times higher as compared to those in 2nd Scenario.
From the point of view of the alpha effect on the plasma equilibrium, important is the ratio of the alpha driven current j α tot with respect to the total plasma current j eq [1] neglecting the fusion alpha contribution. j R Z and of the total plasma current including fusion alpha contribution (solid black lines) in the plasma mid-plane for 2 nd and 4 th Scenario. It is seen that alpha driven current can comprise a significant part of plasma current and in the case of 4 th Scenario can make up to 10-15% of the equilibrium plasma current density without j α tot as calculated by ASTRA [1]. Therefore alpha current can noticeably affect the plasma equilibrium especially in the case of reversed shear plasma in 4 th Scenario. Note that reversed shear induced enhancement of alpha driven current in ITER is in agreement with the current hole enlargement of j α observed in Monte-Carlo modelling of paper [13]. Important from the point of view of the alpha impact on tokamak plasma is the value of total alpha driven current, (1.4) Table 1 represents the calculated values of current induced by alphas, I  , reversed electron current, I e , as well as total alpha driven current, I  tot , for 2 nd and 4 th Scenario. As expected, electrons compensate substantial part of the alpha induced current (~ 0.7MA in 2 nd scenario and 1.2MA in 4 th scenario). As a result the total current driven by fusion alphas is rather low contributing to full toroidal current only < 0.2MA and < 0.5MA in 2 nd and 4 th scenarios respectively. Evidently the alpha driven current will result in small reduction of safety factor ~ I  tot /I, which amounts ~ 5% in 4 th scenario and only ~ 1% in 2 nd scenario.
where R c denotes the major radius of the plasma centre (= 6.2m in 2 nd and 6.35m in 4 th Scenario), ψ is an unperturbed poloidal flux (neglecting j α tot ). According to our estimations the deviation of the approximate alpha driven current from exact one, ψj α tot -j ̑α tot , is rather low. Thus -0.6kA/m 2 < δj < 0.5kA/m 2 for 2 nd Scenario and -3kA/m 2 < δj < 2.5 kA/m 2 for 4 th Scenario Fig.7 displays the profiles of Π (ψ) and Г (ψ) in the case of unperturbed equilibrium configuration [1] and those accounting for Г α (ψ) and Π α (ψ) in 2 nd and 4 th ITER scenarios. It is seen that alpha particles change predominantly P(ψ) while G(ψ) is practically unaffected. Therefore, taking into account j = j eq [R, G(ψ), Π (ψ)] resulting from Eq. (1.5), we conclude that variation of toroidal current Dj eq /j eq induced by j α tot can be estimated as Using expressions of Eq. (1.6) and profiles P(ψ), G(ψ) shown in Fig. 7 we conclude that Dj eq /j eq < 0.03 for 2 nd Scenario and < 0.15-0.20 for 4 th Scenario.
To evaluate quantitatively the alpha impact on magnetic configuration of ITER we compare HELENA calculations of equilibrium in case of unperturbed toroidal current j = j eq [R, G eq (ψ), Π eq (ψ)] and in the case when alpha current is included, i.e. when j = j eq [R, G eq (ψ) + G α (ψ), Π eq (ψ) . Effect of alpha current on the safety factor and the Shafranov shift is illustrated in Figs. 8 and 9. For the 4 th ITER scenario it is seen that the alpha driven current reduces the safety factor in the plasma core by about 15% and enlarges there the Shafranov shift by ~11%.
The present study demonstrates that fusion alphas are expected to induce an additional rotational transform of the magnetic field lines in reactor size tokamak plasmas. In reversed shear plasma scenarios the impact of the alpha driven current appears to be greater. While in the ITER steady state scenario alpha particles induce a 15% reduction of the safety factor q in the core area, in the 2 nd ITER Scenario with positive shear the reduction of q in the core is <3% according to our calculations.
Nevertheless, also such an alteration may reduce the core safety factor, which in Scenario 2 is only 1.02-1.04 [1], to a value below 1, the crucial value for plasma stability [20]. It is noted that, in spite of the low intensity of the total current driven by fusion alphas, j a can play a role of a seed current for the bootstrap tokamak reactor. Evidently, the development of advanced plasma scenarios and research programs for ITER and future tokamak reactors should account for the effects of currents driven by fusion alphas.
Also significant for plasma equilibrium is a partial contribution of fusion alphas to the plasma pressure as well as the anisotropy of the latter. In spite of the relatively low density of energetic alphas as compared to those of bulk plasma components (N α < 8.9·10 17 m -3 < 0.8%n e in 2 nd scenario and less than 6.2·10 17 m -3 < 0.8% n e in 4 th one as seen in Fig.10), their contribution to plasma beta can exceed 10% [1] due to the high energy of alpha particles.
accuracy the current density j α tot (R,Z) can be approximated by the equilibrium-like profile where R c denotes the major radius of the plasma centre (=6.2m in 2 nd and 6.35m in 4 th Scenario),  is an unperturbed poloidal flux (neglecting j α tot ). According to our estimations the deviation of the approximate alpha driven current from exact one, rather low. Thus -0.6 kA/m 2 < j < 0.5 kA/m 2 for 2 nd Scenario and -3 kA/m 2 < j < 2.5 kA/m 2 for 4 th Scenario Fig. 7  The present study demonstrates that fusion alphas are expected to induce an additional rotational transform of the magnetic field lines in reactor size tokamak plasmas. In reversed shear plasma scenarios the impact of the alpha driven current appears to be greater. While in the ITER steady state scenario alpha particles induce a 15% reduction of the safety factor q in the core area, in the 2 nd ITER Scenario with positive shear the reduction of q in the core is <3% according to our calculations. Nevertheless, also such an alteration may reduce the core safety factor, which in Scenario 2 is only 1.02-1.04 [1], to a value below 1, the crucial value for plasma stability [20]. It is noted that, in spite of the low intensity of the total current driven by fusion alphas, j  can play a role of a seed current for the bootstrap tokamak reactor.
Evidently, the development of advanced plasma scenarios and research programs for ITER and future tokamak reactors should account for the effects of currents driven by fusion alphas.
Also significant for plasma equilibrium is a partial contribution of fusion alphas to the ~~ 6 To evaluate the anisotropy of the alpha particle pressure, we consider transverse, p α^, and longitudinal, p αll , components of the pressure tensor [21] (1.7) where p α^ and p αll are given by Scenario 4. Shown in this figure is also a "mean" pressure p α = tr (p ¨ α )/3 = (p α|| + 2p α^) corresponding to the alpha particle contribution to total plasma pressure. It is seen that (p αllp α^) /p αll can exceed 40-45% at low-B side thus introducing substantial (~ 4-5%) anisotropy to total pressure of ITER plasma.
Important in this context are also the electron and ion power deposition profiles, P ae and P ai. Figure 12 compares the poloidal profiles of alpha power deposited to electrons for 2 nd and 4 th scenario. As expected, magnetic reversed shear in 4 th scenario results in broadening and in reduction of P αe as compared to those in 2nd scenario. Powers deposited to the bulk plasma ions P αd and P αt are small and comprise, respectively, less than 20% and 15% of P αe .

COLLISIONAL LOSS OF DT ALPHAS
For evaluation of the fusion alpha impact on the first wall of ITER important is the predictive modelling of the alpha loss. In spite of the low level of the first orbit losses in ITER the collisional ones are significant. Figure 13 represents the fraction of fusion alphas, L(E), lost at energies greater than E as well as the energy spectra of these particles, EdL(E)/dE, for the 2 nd and 4 th ITER scenario.
It is seen that alphas with energy ranges 3MeV<E<3.5MeV and 0.5MeV<E<1MeV contributes predominantly to collisional losses. It is important to note that at rather high energies E>1MeV alpha losses for 2 nd scenario (with small radial excursions of alphas) exceed those for 4 th scenario (with large radial excursions of alphas). This is due to extremely low level of fusion production at the plasma periphery (r > 0.7a) in the case of 4 th scenario [1] shown in Fig.1d. However, in wider energy range 0.3MeV<E<3.5MeV the total collisional loss fraction of alphas for the 4 th scenario is about 31% contrary to only 24% loss fraction for the 2 nd scenario. Note that enhanced collisional energetic alphas as compared to those of bulk plasma components (N  < 8.9·10 m < 0.8%n e in 2 nd scenario and less than 6.2·10 17 m -3 < 0.8% n e in 4 th one as seen in Fig. 10), their contribution to plasma beta can exceed 10% [1] due to the high energy of alpha particles.
To evaluate the anisotropy of the alpha particle pressure, we consider transverse, p α , and longitudinal, p αll , components of the pressure tensor [21]   where p α and p αll are given by 2 2 , 2 b=B/B, B is the magnetic field and I is the unit dyad. In expressions (1.8) we take into account the gyrotropic structure of the alpha particle distribution function, 10 for Scenario 4. Shown in this figure is also a "mean" pressure corresponding to the alpha particle contribution to total plasma pressure. It is seen that (p αll -p α )/p αll can exceed 40-45% at low-B side thus introducing substantial (~ 4-5%) anisotropy to total pressure of ITER plasma.
Important in this context are also the electron and ion power deposition profiles, P e and P i. Fig. 12 compares the poloidal profiles of alpha power deposited to electrons for 2 nd and 4 th scenario. As expected, magnetic reversed shear in 4 th scenario results in broadening and in reduction of P αe as compared to those in 2nd scenario. Powers deposited to the bulk plasma ions P αd and P αt are small and comprise, respectively, less than 20% and 15% of P αe . in 2 scenario and less than 6.2·10 m < 0.8% n e in 4 one as seen in Fig. 10), their contribution to plasma beta can exceed 10% [1] due to the high energy of alpha particles.
To evaluate the anisotropy of the alpha particle pressure, we consider transverse, p α , and longitudinal, p αll , components of the pressure tensor [21]   where p α and p αll are given by 2 2 , 2 b=B/B, B is the magnetic field and I is the unit dyad. In expressions (1.8) we take into account the gyrotropic structure of the alpha particle distribution function, 10 for Scenario 4. Shown in this figure is also a "mean" pressure corresponding to the alpha particle contribution to total plasma pressure. It is seen that (p αll -p α )/p αll can exceed 40-45% at low-B side thus introducing substantial (~ 4-5%) anisotropy to total pressure of ITER plasma.
Important in this context are also the electron and ion power deposition profiles, P e and P i. Fig. 12 compares the poloidal profiles of alpha power deposited to electrons for 2 nd and 4 th scenario. As expected, magnetic reversed shear in 4 th scenario results in broadening and in reduction of P αe as compared to those in 2nd scenario. Powers deposited to the bulk plasma ions P αd and P αt are small and comprise, respectively, less than 20% and 15% of P αe .
To evaluate the anisotropy of the alpha particle pressure, we consider transverse, p α , and longitudinal, p αll , components of the pressure tensor [21]   where p α and p αll are given by 2 2 , 2 b=B/B, B is the magnetic field and I is the unit dyad. In expressions (1.8) we take into account the gyrotropic structure of the alpha particle distribution function, 10 for Scenario 4. Shown in this figure is also a "mean" pressure corresponding to the alpha particle contribution to total plasma pressure. It is seen that (p αll -p α )/p αll can exceed 40-45% at low-B side thus introducing substantial (~ 4-5%) anisotropy to total pressure of ITER plasma.
Important in this context are also the electron and ion power deposition profiles, P e and P i. Fig. 12 compares the poloidal profiles of alpha power deposited to electrons for 2 nd and 4 th scenario. As expected, magnetic reversed shear in 4 th scenario results in broadening and in reduction of P αe as compared to those in 2nd scenario. Powers deposited to the bulk plasma ions P αd and P αt are small and comprise, respectively, less than 20% and 15% of P αe .

g-EMISSION INDUCED BY FUSION ALPHAS
Finally Fig.14 demonstrates the mid-plane profiles of partly thermalized alphas with energy E>1.9MeV and profiles of g-emission rates R g from 9 Be(a,ng) 12 C reactions induced by alphas with energies E>1.7MeV, given by (1.9) In Eq. (1.9) n Be represents the density of the Be impurity, the distribution function f α (R,Z,E,x) refers to fusion alphas and s g αBe denotes the cross-section of 9 Be(a,ng) 12 C reaction. It is seen that for both scenarios collisional transport results in essential broadening of the mid-plane profiles of partly thermalized alphas compared to the initial profiles of alphas at birth energy. The fact that the g-ray emission profiles are almost identical to the density profiles of partly thermalized alphas illustrates the value of this particular diagnostic technique.

SUMMARY
Present predictive Fokker-Planck modelling of fusion alphas in ITER demonstrates the prominent sensitivity of their phase space distributions to the plasma scenarios. Thus significant dissimilarity of distributions over R, Z spatial coordinates and over the longitudinal energy is observed for the 2 nd and 4 th ITER scenario. Particularly the longitudinal anisotropy of alpha distributions in 4 th scenario results in rather strong alpha driven current that consists up to 10-15% of the equilibrium plasma current density. Consequently fusion alphas are expected to induce an additional rotational transform of the magnetic field lines in reactor size tokamak plasmas. In reversed shear plasma scenarios the impact of the alpha driven current appears to be greater. While in the ITER steady state scenario alpha particles induce a 15% reduction of the safety factor q in the core area, in the 2nd ITER Scenario with positive shear the reduction of q in the core is <3% according to our calculations. Nevertheless, such an alteration may reduce the core safety factor, which in Scenario 2 is only 1.02-1.04 [1], to a value below 1, the crucial value for plasma stability [20]. Alpha driven current shown also to result in essential (~11% in 4th Scenario) enlargement of the Shafranov shift.
It is noted that, in spite of the low intensity of the total current driven by fusion alphas, j α can play a role of a seed current for the bootstrap tokamak reactor. Evidently, the development of advanced plasma scenarios and research programs for ITER and future tokamak reactors should account for the effects of currents driven by fusion alphas.
Anisotropy of the alpha particle pressure (p αllp α^) /p α^ can exceed 40-45% at low-B side of plasma in Scenario 4 thus introducing substantial (~4-5%) anisotropy to total plasma pressure.
The poloidal profiles of alpha density as well as of the fusion power deposition to electrons and ions are found to be profoundly sensitive to operational scenarios. Powers deposited to the bulk JET plasma [8] as well as predicted in ITER in presence of TF ripples [22,23].

5. -emission induced by fusion alphas
Finally Fig. 14 demonstrates the mid-plane profiles of partly thermalized alphas with energy E>1.9MeV and profiles of -emission rates R  from 9 Be(,n) 12 C reactions induced by alphas with energies E>1.7MeV, given by In Eq. (1.9) n Be represents the density of the Be impurity, the distribution function f  (R,Z,E,) refers to fusion alphas and Be    denotes the cross-section of 9 Be(,n) 12 C reaction. It is seen that for both scenarios collisional transport results in essential broadening of the mid-plane profiles of partly thermalized alphas compared to the initial profiles of alphas at birth energy.
The fact that the -ray emission profiles are almost identical to the density profiles of partly thermalized alphas illustrates the value of this particular diagnostic technique.
|| plasma ions are small and consist less than 1/3 of those deposited to electrons. Radial profiles of g-emission rates from 9 Be(a,ng) 12  McClements for fruitful discussions on alpha driven current and alpha impact on plasma equilibrium.

3. Alpha-particle impact on the plasma equilibrium and on the bulk plasma parameters
In spite of the rather low effect of total current driven by fusion alphas, j α may result in a consequential redistribution of the toroidal current in the plasma core and thereby alter the plasma equilibrium in addition to I  tot induced enhancement of rotational transform (reduction of safety factor). To demonstrate this we use the code HELENA [19] to evaluate the alpha current effect on the safety factor and the Shafranov shift. Note that with reasonable