Dependence of Potential Well Depth on the Magnetic Field Intensity in a Polywell Reactor
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- Kazemyzade, F., Mahdipoor, H., Bagheri, A. et al. J Fusion Energ (2012) 31: 341. doi:10.1007/s10894-011-9474-4
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Using OOPIC-Pro assisted-two dimensional simulation we have considered the dependencies of the electron and ion densities, as well as the central electric potential on the magnetic-field intensity in the Polywell fusion reactor. It is shown that the potential well depth increases with decreasing the magnetic intensity, while much narrower well width (thus more effective deuteron trapping) is achieved with increasing the magnetic field intensity. The results obtained can be employed to adjust the magnetic field intensities at which more effective electron confinement, thus more effective ion-flux convergence, is expected. Furthermore, this study can be used to reach the optimized conditions of the reactor operation as well as to relate to the next generation fusion fuels.
KeywordsPolywell fusion reactor Particle-in-cell code Negative potential well (NPW) Magnetic field intensity
Negative potential well
Polywell is an inertial electrodynamics confinement fusion reactor with an easy conceptual design registered by Bussard . This reactor had been designed based on electrostatic confinement fusion (IECF) device and was an improved version of it. Virtual cathode formation at the reactor center (formation of a dens electron cloud), due to confining electrons by strong-enough external magnetic field, is an essential mechanism through operation of this device. Potential well, created by the high-density electron cloud, accelerates the produced ions from all direction towards the center, where they meet each other, and as a result fusion reactions occur, or the ions may be scattered. If the ions are scattered, then they return to the center due to potential well attraction, and finally incorporate in the fusion reactions after multiple round trips. Effective saving of lost electrons due to magnetic mirror effect, establishing electron (input and loss) fluxes balance, and efficient self-stabilizing of magnetic geometry (as a result of its convex nature) are among many advantages brought by Polywell fusion reactor.
Several experimental and simulation studies, so far, have been carried out toward improving the electrostatic confinement reactors. Increasing in neutron yield via additional electrode inside the cathode, which suppresses the virtual anode formation at high currents, is reported by Noborio et al. . Takamatsu et al.  reported a ten-times increase in number of fusion reactions as well as an increase in overall efficiency, all when ion sources were employed in the setup. The control of the ion motions during the device operation by applying an axial magnetic field was simulated by Tomiyasu et al. . Following these studies, Kurilenkov et al.  investigated the effects of virtual cathode, and single- and double-well potentials on the IECF reactor operation when an electric discharge is applied. Finally, the most recent experimental work by Damideh et al.  on IECF reactor (as a continuous fusion reaction device), which operated at -140 kV voltage and 70 mA current, resulted in 2 × 107 D-D reactions per second.
Nevertheless, there are a few reports on the electrodynamics confinement devices (e.g., Polywell reactor). Besides the experimental and theoretical reports made by Bussard and his coworkers at EMC2 (Energy Matter Conversion Corporation), there are limited literature for this research field. Recently, Rogers has provided insights towards obtaining scaling rule, estimating an exact potential-well depth, and optimizing the device operation . Moreover, the experimental studies on Polywell reactors have been carried out only on the small size setup. The investigation of the effects of variations in the coil current and background gas pressure on the virtual cathode behavior, which was done out by Carr et al.  is among these studies. To the best of our knowledge, there is no report on potential well behavior under magnetic-field-strength variation. So, in this work, the effect of magnetic field strength on the potential well depth is investigated using OOPIC-Pro two-dimensional (2D) code, which has been broadly used by many authors [9, 10, 11, 12, 13]. Moreover, PIC simulation was used by Bussard but the results were not published as he mentioned in his paper at IAC conference .
This paper is organized in this fashion. In Sect. “Simulation Model” the geometry of the device simulated is described. The simulation results are presented and discussed in Sect. “Results and Discussion”. The results obtained are summarized and finally the article concludes with an outlook for future research.
Main simulation parameters
Vacuum tank dimensions
1.4 × 1.4 m2
Electron gun current
Electron gun potential
Ion gun current
Ion gun potential
The simulation starts with an empty tank and as time goes on the tank is filled with electrons, being emitted from electron guns (directed along the face cusps, see Fig. 1b), which pass through the face cusps and are converged radially by the magnetic field to the center region, the so-called electron confinement. This magnetic field assisted-electron confinement leads to formation of a high density electron cloud, so that the electron kinetic energies are completely transformed into a negative potential energy-appearance of a deep potential well-which is becoming deeper(due to electron density increase) as time passes. In the same time, the Hydrogen ions produced (and derived) by ion guns (within the coil configuration) are repulsed towards the center by the positive coil potential. This is why the ion guns are located between the coils, otherwise it may be impossible to direct ions towards the center. This ion acceleration (towards the center) also becomes more effective via ion trapping in the potential well so that, finally, all deuterons become mono-energetic species. As a result, the ion density increases at the center, which in turn the fusion reaction rate becomes higher. The scattered ions pass through the electron cloud formed and are slowed down, again are attracted towards the center, so that they finally hit other trapped ions and fuse.
Results and Discussion
In this section we present the results of the simulation of the electron cloud formation and its effects on the potential and ion density profiles for two cases of low and high magnetic strengths.
Low Magnetic Field Condition
Here, the electrons have been distributed in the wide central region and the electron density at the magrid corners is remarkable, indicating an effective electron loss at the corner. The ion density increase at the center, which is clearly shown in Fig. 3b, describe the efficient ion trapping due to ion dropping at the center of the negative potential well (NPW).
High Magnetic Field Condition
By applying such high magnetic field, the electron density ρe tends to much higher values (2.9 × 1012 cm−2) at the center. In response to this electron density increase (and as a result much deeper NPW expected), more effective convergence concentration of hydrogen ions takes place in much smaller region at the Polywell reactor center, which in turn leads to much higher positive energy, and thus decreasing the magnitude of the negative potential.
Thus, we have simulated the plasma environment of the Polywell fusion reactor using OOPIC-Pro program. Using the program, we have shown that the potential-well behavior strongly depends on the strength of the applied external magnetic field. The magnitude of NPW surprisingly becomes lower with increasing the strength, while the well width decreases, confirming more effective confinement of the electrons (due to much higher magnetic strength generated). At high magnetic field intensities, an efficient electron confinement and less effective electron loss happen, leading to an effective radial convergence of hydrogen ions to the center, which is impossible with a low-density electron cloud (created by weak magnetic fields). The results obtain can be used to optimize the operation of the future Polywell fusion reactors towards net-power generation. More importantly, the main conclusions are not restricted to the D–D fuel and may be relevant to the broader range of the fusion fuels (D-T and p-B11) will be used in Polywell fusion reactor plans, which may be the aim of our future works.