PUBLISHED Electricpotentialinamagneticallyconfinedvirtualcathodedevice

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/350595180
Electric potential in a magnetically confined virtual cathode fusion device
ArticleinPhysics of Plasmas · April 2021
DOI: 10.1063/5.0040792
CITATIONS
0
READS
6
2 authors, including:
Some of the authors of this publication are also working on these related projects:
Miniature microwave plasma antenna at 2.45 GHz View project
Richard Bowden-Reid
The University of Sydney
4 PUBLICATIONS21 CITATIONS
SEE PROFILE
All content following this page was uploaded by Richard Bowden-Reid on 17 May 2021.
The user has requested enhancement of the downloaded file.

Phys. Plasmas 28, 042702 (2021); https://doi.org/10.1063/5.0040792 28, 042702
© 2021 Author(s).
Electric potential in a magnetically confined
virtual cathode fusion device
Cite as: Phys. Plasmas 28, 042702 (2021); https://doi.org/10.1063/5.0040792
Submitted: 16 December 2020 . Accepted: 11 March 2021 . Published Online: 02 April 2021
Richard Bowden-Reid, and Joe Khachan
ARTICLES YOU MAY BE INTERESTED IN
An inertial electrostatic confinement fusion system based on graphite
Physics of Plasmas 28, 042703 (2021); https://doi.org/10.1063/5.0038766
Electron kinetics in low-temperature plasmas
Physics of Plasmas 26, 060601 (2019); https://doi.org/10.1063/1.5093199
Measurements and modeling of ion divergence from a gridded inertial electrostatic
confinement device using laser induced fluorescence
Physics of Plasmas 27, 103501 (2020); https://doi.org/10.1063/5.0002916

Electric potential in a magnetically confined virtual
cathode fusion device
Cite as: Phys. Plasmas 28, 042702 (2021); doi: 10.1063/5.0040792
Submitted: 16 December 2020 .Accepted: 11 March 2021 .
Published Online: 2 April 2021
Richard Bowden-Reid
a)
and Joe Khachan
b)
AFFILIATIONS
Department of Plasma Physics, School of Physics, University of Sydney, Sydney 2006, Australia
a)
Author to whom correspondence should be addressed: [email protected]
b)
[email protected]
ABSTRACT
The magnetically confined virtual cathode (MCVC) is an approach to nuclear fusion in which multipole magnetic traps are used to confine a
dense cloud of electrons and thereby establish a deep electrostatic potential well for the heating and trapping of ions. We describe
preliminary studies conducted in MCVC-0, a two-coil, biconic cusp trap, in which high impedance, floating Langmuir probe measurements
were used to characterize the electrostatic potential. Contrary to previous studies in six-coil “polywell” devices, no potential well formation
was observed and this is attributed to the particular configuration of magnetic fields within the new device. A computational model was
developed, based on the anisotropic electrical conductivity of discharge plasmas within magnetic fields, and shown to accurately describe the
obtained experimental results. Electrostatic boundaries that were intersected by magnetic field lines were found to strongly dominate the
form of the electric potential within the device, with strong implications for the design of future MCVC/polywell machines.
Published under license by AIP Publishing. https://doi.org/10.1063/5.0040792
I. INTRODUCTION
Inertial electrostatic confinement (IEC) is a method of producing
nuclear fusion wherein a spherically convergent electric field is used to
heat and trap ions. First proposed by Oleg Lavrent’ev in 1950,
1–4
the
approach uses two or more spherically concentric electrodes to mimic
the radial gravitational well present in stars. Although Lavrent’ev’s
machine was never built in the Soviet Union, American inventor Philo
Farnsworth independently devised and tested a similar device.
5
Robert
Hirsch and Gene Meeks, working under Farnsworth, also successfully
demonstrated a small scale electric fusion device based on Lavrent’ev’s
concept.
6–8
Obtaining nuclear fusion in an IEC device is almost trivial when
compared to standard, thermonuclear style devices due to the ease
with which high energy ions (25–100 kV) may be obtained simply by
increasing the applied system voltage. Small scale, deuterium fueled
machines routinely achieve neutron production rates of 106–108s
1
in steady state operation and hence a great many IEC systems have
been operated in the United States,
9–14
Japan,
15–20
Australia,
21–24
Germany,
25
Denmark,
26
the Netherlands,
27
Iran,
28–30
and Turkey.
31
While the devices find use as small scale neutron generators for the
production of medical isotopes, neutron imaging, and security applica-
tions,
13,32–34
theoretical studies by Rider
35
and Nevins
36
indicate little
opportunity for net energy production. It has been noted by other
authors, however,
37,38
that the assumptions made by Rider and Nevins
in their analyses may be overly pessimistic and in some cases are self-
contradictory, and that a net energy gain in IEC is, in principle,
possible.
The polyhedral well machine, or polywell, is a hybrid electromag-
netic device that was devised with the view to circumvent the losses of
gridded IEC machines.
39,40
Invented by Robert Bussard,
41,42
the device
makes use of magnetic cusp trapping to confine a dense population of
electrons, thereby generating a virtual cathode. The requirement that
only electrons need be magnetically confined relaxes the design
requirements on such a trap, in terms of both size and magnetic field
strength, when compared with conventional thermonuclear machines.
Further, the absence of grid electrodes enables a higher degree of ion
recirculation within the core and hence the probability of fusion for
any given ion is greatly increased.
Bussard described a device in which magnetic field coils are posi-
tioned on the faces of a regular polyhedron, most commonly a cube.
The coils are oriented such that their magnetic moments point
inwards, resulting in a high order multipole cusp with a central mag-
netic null. High energy electrons are injected into the core from elec-
tron guns placed outside of the magnet coils and the resulting build-
up of negative space charge produces the desired virtual cathode or
“potential well.” Bussard reasoned that if the kinetic plasma pressure
Phys. Plasmas 28, 042702 (2021); doi: 10.1063/5.0040792 28, 042702-1
Published under license by AIP Publishing
Physics of Plasmas ARTICLE scitation.org/journal/php

withinthedevicecouldbemadetoapproachthemagneticpressure,
that is if
b¼Pplasma
Pmagnetic ¼nkBT
B2=2l0!1;(1)
then the diamagnetic circulation of electrons about magnetic field lines
would expel the applied field from the core. This “high beta” mode,
sometimes referred to as the “Wiffle ball” after the popular American
children’s toy, was expected to exhibit the favorable particle trapping
properties first described by Grad and Berkowitz
43,44
leading to a sharp
increase in device performance once the high beta mode was obtained.
A number of low beta polywell devices have also been operated
at The University of Sydney (USYD).
45–51
The work has been princi-
pally concerned with the phenomenon of potential well formation and
characterization of the electron trapping properties of the polywell
field configuration. The first USYD polywell, constructed by Carr,
45
consisted of teflon reels fastened together by aluminum brackets.
Electrons were injected using a hollow cathode style electron gun
52
and floating Langmuir probe measurements showed 100–200 V
potential wells over a broad range of background gas pressures. Carr
subsequently upgraded his machine using toroidal aluminum coil
cases that were conformal to the magnetic field. The resulting machine
operated at lower voltages than its predecessor (100–200 V) but pro-
duced potential wells of comparable relative depth (10–20 V). Carr
also used biased Langmuir probe measurements to characterize the
energies of the trapped electrons and proposed a novel energy distri-
bution function.
47
Cornish
49,50
conducted a survey of scaling laws
within the Polywell, with particular consideration given to the depen-
dence of virtual cathode formation on the size and spacing of the mag-
netic field coils. Finally, studies conducted by Ren and Poznic
51
examined electron density and energy distributions in a larger device
using both biased Langmuir probe and radio frequency plasma wave
techniques.
In this paper, we detail the operation of magnetically confined
virtual cathode (MCVC-0), the University of Sydney’s most recent
polywell-style machine. MCVC-0 represents both the largest and high-
est power virtual cathode fusion experiment at the University of
Sydney and was designed to operate in a parameter regime (in terms
of applied voltages and plasma currents) where measurable deuter-
ium–deuterium fusion was possible. Due to size limitations, this
machine consists of two magnetic field coils, rather than the traditional
six, arranged such that they form a biconic cusp. As such, the device
maynolongerbereferredtoasapolywell, and hence we adopt the
more generalized nomenclature magnetically confined virtual cathode.
In Sec. II, we describe the MCVC-0 system and the associated diagnos-
tics. In Sec. III, we present results from single-ended floating probe
measurements of the MCVC-0 plasma and illustrate significant dis-
crepancies between the measured electrostatic profiles and the
expected potential wells. In Sec. IV, we outline a theoretical model
based on the solution of the Poisson equation in the presence of a con-
ductive medium and demonstrate how anisotropic plasma conductiv-
ity sufficiently accounts for the unexpected behavior of the MCVC-0
machine. It is found that the electric potential within the device is
dominated by those electrostatic boundaries that are intersected by
magnetic field lines, which has significant implications for the design
of future MCVC/polywell style fusion machines.
II. APPARATUS
A. MCVC-0 device
The MCVC-0 device was constructed within a cylindrical vacuum
chamber 300 mm in diameter and 300 mm in length. A pair of
100 turn magnetic field coils (152 mm diam, 1770 lHand0:15 X)
were situated within toroidal metal cases, which were the positive elec-
trodes in the MCVC-0 system. The tori were constructed from 316
stainless steel and had major and minor radii of approximately 76 and
30 mm, respectively, and a wall thickness of 4 mm. In order to allow
biasing of the cases relative to the field coils, the coils were supported
freefloatingwithinthetoriusingsetsofinterlockinginsulatingcollars
made from polyether–ether–ketone (PEEK). The coils were mounted
on a support frame consisting of a pair of stainless steel plates fastened
together by three vertical struts. The magnetic field coils were mounted
to the frame on PEEK bushings, such that the cases could be biased
610 kV relative to the support structure. The PEEK supports were
machined with multiple fins to increase the arc creep distance and
were sheathed in 60 mm O.D. alumina ceramic tube to prevent sput-
tering damage. In order to improve the high vacuum compatibility of
the apparatus, all steel components were baked at 500 Cfor72h.The
coil support structure is depicted in Fig. 1. Note that the magnetic field
lines within the device are everywhere conformal to the toroidal cases
such that particle collection on the electrodes occurs transverse to the
magnetic field. This so-called “magnetic shielding” reduces the col-
lected current during a shot, thereby improving the efficiency of the
device.
The magnetic field coils were driven by a 108 mF, 900 V capaci-
tor bank resulting in a maximum coil current of 2000 A. The peak
achievable magnetic field strength, when measured in the center of the
coils, was 1.15 T. The coil cases were biased at a maximum voltage of
6 kV, switched to the cases from a 180 lF capacitor using a MOSFET
switch. Electron beam injection was necessary for the formation of a
virtual cathode. A thermionic electron source was therefore con-
structed in the lower, axial vacuum port such that electrons could be
injected through the face of the lower magnetic field coils. A custom
filament support stage was positioned within the lower port of the vac-
uum chamber and populated with six 12 V, 50 W tungsten filaments
obtained from halogen light bulbs. The filament stage was supported
on ceramic rods such that it could be biased to 2000 V with respect
to the vacuum chamber. A grounded molybdenum mesh spanned the
port opening to accelerate the thermionic electrons into the chamber.
Theentireelectrongunassemblywassheathedwitha62mminside
diameter borosilicate glass tube in order to provide additional electrical
standoff between the floating filament stage and the wall of the vac-
uum port. In all experiments the electron gun current was set to its
maximum value of 150 mA, at an injection energy of 1 kV. The total
energy gained by an electron as it enters the core of the device is there-
fore the applied coil bias plus 1 keV.
Prior to all experiments, the MCVC-0 system was pumped down,
with baking at 165 C, until the ultimate base pressure of
1107Torr was reached. Optical spectra obtained during plasma
shots at base pressure were found to be dominated by strong HaH
Balmer lines, identifying the primary gas component as residual atmo-
spheric water. All experimental runs were therefore conducted without
the addition of hydrogen or deuterium gas and hence all presented
results were obtained using the base system pressure of
1107Torr. During a typical shot, the electron gun was activated
Physics of Plasmas ARTICLE scitation.org/journal/php
Phys. Plasmas 28, 042702 (2021); doi: 10.1063/5.0040792 28, 042702-2
Published under license by AIP Publishing

and allowed to heat for 2–3 s such that the thermionic emission stabi-
lized. The high voltage (HV) bias was switched to the coils for a dura-
tion of 400 ms and the magnetic coils were fired at the mid-point of
the HV pulse. An example shot trace is given in Fig. 2.Asingle-ended
floating Langmuir probe was positioned at the core of the device and
the resulting trace is given in red. The floating potential in the core is
seen to mirror the applied bias voltage up to time t¼0atwhichpoint
the magnetic field pulse (given in black) causes a sharp drop. Magnetic
trapping of electrons in the core results in a build of negative space
charge and hence the reduction in floating potential. As the magnetic
field pulse decays, the floating potential is once again seen to rise as
the trapped virtual cathode dissipates. Note that before (t<200 ms)
and after (t>200 ms) the HV pulse, both the coil cases and floating
probe are charged negatively by the electron gun beam.
B. High impedance floating Langmuir probe
A Langmuir probe was assembled from telescoping sections of
alumina ceramic tubing, sealed using TorrSeal adhesive and installed
in a translational stage such that it could be precisely positioned within
the vacuum chamber. The exposed probe tip consisted of a 50 lm
diameter, 5 mm long cylindrical tungsten wire.
The spatial distribution of relative electric potentials was obtained
through measurement of the floating potential, V
f
, obtained by con-
necting the Langmuir probe, via a 2 GXseries resistor, directly to an
oscilloscope input. The oscilloscope channel is terminated internally
by a 1 MXinput resistor in parallel with a 13 pF capacitance. The
resulting RRC circuit acts as a 2001:1 voltage divider between the
probe tip and ground up to a roll-off frequency of 12 kHz. The tem-
poral response of the probe is therefore very short relative to the time-
scale of a plasma shot. The floating potential is always smaller than the
space potential and may be approximated, for a Maxwellian plasma, as
VfVskBTe
2eln 2mi pme
;(2)
where k
B
is the Boltzmann constant, T
e
is the electron temperature, e
is the fundamental charge and m
e
and m
i
are the electron and ion
masses, respectively.
53
For hydrogen, deuterium and water the loga-
rithmic factor is about 7.1, 7.7, and 9.9, respectively. The floating
potential is therefore only a valid measure of the space potential in sys-
tems where the electron temperature, T
e
, does not vary significantly
with time and the electron velocity distribution does not contain a
non-thermalized, high energy beam components. In systems where
ðkBTe=eÞVs, however, the floating potential serves as a convenient
FIG. 1. Magnetically confined virtual cath-
ode machine.
Physics of Plasmas ARTICLE scitation.org/journal/php
Phys. Plasmas 28, 042702 (2021); doi: 10.1063/5.0040792 28, 042702-3
Published under license by AIP Publishing