# Inertial Electrostatic Confinement Fusion Reactor done.docx

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Published on 22 Apr 2013
School
Queen's University
Department
Engineering Physics Courses
Course
ENPH 455
Professor
Page:
of 50
1
Simulation and Optimization of an Inertial
Electrostatic Confinement Fusion Reactor
by
Jimmy Zhan
A thesis submitted to the Department of Physics, Engineering Physics and Astronomy in
conformity with the requirements of ENPH 455
Supervisor: Dr. Robert Knobel
Faculty of Applied Science and Engineering
Queen's University
April 2, 2013
2
Abstract
The Inertial Electrostatic Confinement Fusion Reactor (IEC Fusion) is a potential method for
controlled fusion power. The IEC fusion reactor confines plasma via a strong electrostatic
potential between two concentric grids as ions stream towards the center. The electrostatic
potential between the outer grid and the inner grid is on the order of magnitude of tens of kilo
volts, and the outer grid is usually grounded. Gas species such as Deuterium and Tritium are
injected into a vacuum chamber housing the grids, usually at pressures on the order of a millitorr.
Once ionized by the electric field, the ions accelerate radially toward the central grid, colliding
with other ions of sufficient relative velocity to undergo fusion. Those ions that shoot through the
center without fusing will decelerate and fallback towards the center, making another pass. This
method of confinement therefore has two advantages: Plasma recirculates around the central grid
making multiple passes and hence increasing the likelihood of fusion. Optimal fusion cross
section is on the order of hundred million Kelvins, while difficult to achieve conventionally, it
translates to only tens of kilo electron volts, which is fairly easy to achieve via electrostatics.
There are also difficulties associated with IEC fusion. Several loss mechanisms limit its ultimate
power output, the most significant being Coulomb interactions, causing bremsstrahlung radiation
and thermalization of ion velocities, and ion-grid collisions. This thesis investigates the fusion
performance of a cylindrical IEC device, this will be done via computational modelling, and
iterative numerical simulations of performance parameters. A set of optimum design parameters
will be derived from the simulations, and a preliminary design for an IEC device will be given.
The results were not surprising, there is an optimum operating voltage of approximately 190 kV.
The optimum pressure and chamber size is approximately 1 meter at 1 millitorr. The grid
transparency has a dramatic effect on the performance as well, but this is material limited to
98%. A novel method of reducing grid collisions is being researched by the US Navy currently,
in which electrons are trapped to form a virtual cathode, using magnetic fields. This is termed the
Polywell.
3
List of Figures
Figure 1 The original Farnsworth fusor. ....................................................................................................... 9
Figure 2 Hirsch-Meeks fusor. ....................................................................................................................... 9
Figure 3 The correct model for fusion cross section [10]. .......................................................................... 12
Figure 4 Coulomb interaction and Bremsstrahlung radiation of an electron and ion [10] .......................... 14
Figure 5 Charge exchange process of various isotopes of Hydrogen [15].................................................. 15
Figure 6 Comparison of fusion performance of various anode-cathode geometries [29]. .......................... 16
Figure 7 The simulation reached near steady state in approximately 10 μs, with the number of ions and
electrons equal. [29] .................................................................................................................................... 17
Figure 8. Ion-ion reactions occur only inside the inner grid, ion-neutral collisions rate increases
approaching the center, and neutral-neutral collisions occur uniformly throughout device. [29] .............. 17
Figure 9 A total neutron flux of roughly 8.8∙10^5 n/s was achieved, at a grid voltage of 100 kV and
current of 40 mA. [29] ................................................................................................................................ 18
Figure 10 The basic schematic of an IEC fusion reactor [16]. .................................................................... 21
Figure 11 The simulation cell, containing one macro-particle [21]. ........................................................... 22
Figure 12 The Leapfrog method, showing the time offset between position and velocity [21]. ................ 24
Figure 13 The dependence of fusion rate as a function of grid voltage. The fuel pressure is kept at 0.001
millitorr, and the chamber radius is 1 m. .................................................................................................... 27
Figure 14 The dependence of the fusion rate plotted against the cathode grid transparency. Note that this
is a log plot. The voltage is at 60 kV, the fuel pressure is kept at 0.001 millitorr, and the chamber radius is
1 m. ............................................................................................................................................................. 28
Figure 15 The dependence of fusion rate on the input fuel gas pressure. The voltage is kept at 60 kV, and
the chamber radius at 1 m. .......................................................................................................................... 29
Figure 16 The dependence of fusion rate on the chamber size. The voltage is at 60 kV, and the pressure is
at 0.001 millitorr. ........................................................................................................................................ 30
Figure 17 The Paschen Curve for various gases, illustrating the “Paschen Minimum”. The breakdown
voltage of air on either side of the minimum value has inverse relationship with the product of pressure
and distance. [32] ........................................................................................................................................ 31
Figure 18 Optimum Design. ....................................................................................................................... 32
Figure 19 Optimum Design ........................................................................................................................ 32
Figure 20 Fusion Rate of Optimum Design. ............................................................................................... 33
Figure 21 Definition of the hard-sphere cross section model [10]. ............................................................. 38
Figure 22 The Coulomb force repels, the nuclear force attracts, but only acts at a short range [10]. ......... 39
Figure 23 The classical model of fusion cross section [10]. ....................................................................... 40
Figure 24 The correct model of fusion cross section, including the effects of tunneling, resonance, and
high-speed decay [10]. ................................................................................................................................ 41
Figure 25 Experimentally measured cross sections σ(v) for various fusion reactions of interest. Notice that
DT has a peak of 5 barns at 120 keV, and is clearly favorable in comparison to DD [10]. ........................ 41
Figure 26 <σv> for various fusion reactions of interest, as functions of temperature. Note that the peak
cross section for DT is at 70 keV [10]. ....................................................................................................... 42

## Document Summary

A thesis submitted to the department of physics, engineering physics and astronomy in conformity with the requirements of enph 455. The inertial electrostatic confinement fusion reactor (iec fusion) is a potential method for controlled fusion power. The iec fusion reactor confines plasma via a strong electrostatic potential between two concentric grids as ions stream towards the center. The electrostatic potential between the outer grid and the inner grid is on the order of magnitude of tens of kilo volts, and the outer grid is usually grounded. Gas species such as deuterium and tritium are injected into a vacuum chamber housing the grids, usually at pressures on the order of a millitorr. Once ionized by the electric field, the ions accelerate radially toward the central grid, colliding with other ions of sufficient relative velocity to undergo fusion. Those ions that shoot through the center without fusing will decelerate and fallback towards the center, making another pass.