Feasibility Studies of Alpha-Channeling in Mirror Machines Page: 3 of 12
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Feasibility Studies of Alpha-Channeling in Mirror Machines
A. I. Zhmoginov* and N. J. Fischt
Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
The linear magnetic trap is an attractive concept both for fusion reactors and for other plasma
applications due to its relative engineering simplicity and high-beta operation. Applying the a-
channeling technique to linear traps, such as mirror machines, can benefit this concept by efficiently
redirecting a particle energy to fuel ion heating or by otherwise sustaining plasma confinement,
thus increasing the effective fusion reactivity. To identify waves suitable for a-channeling a rough
optimization of the energy extraction rate with respect to the wave parameters is performed. After
the optimal regime is identified, a systematic search for modes with similar parameters in mirror
plasmas is performed, assuming quasi-longitudinal or quasi-transverse wave propagation. Several
modes suitable for a particle energy extraction are identified for both reactor designs and for proof-
Alpha particles born through D-T fusion reactions
carry 20% of the overall fusion energy. The energy of
the a particle population trapped in a mirror fusion re-
actor largely dissipates through collisions with electrons
or it may excite plasma instabilities (see, for example,
[1 7]). The collisional relaxation of a particles occurs on
a characteristic a-electron collisional time of order of a
second and results in fusion ash buildup. Plasma instabil-
ities excited by a particles, in turn, heat the background
plasma [8 10] and increase the plasma transport, which
also increases the wall heat load.
Alpha-channeling is a wave-particle manipulation tech-
nique, which might be capable of inducing a particle
flows in phase space leading to quick a ejection accom-
panied by a particle cooling. As a result, the energy
with which a particles are born can be transferred to the
waves and then used to sustain the fusion reaction in the
device. The channeling of the a power in one simple mir-
ror configuration  at ignition has been estimated 
to increase, potentially, the effective fusion reactivity by
a factor of 2.8.
In this paper, we discuss and reformulate the results
of our previous studies concerning a-channeling in mir-
ror machines. In addition, using a more convenient set
of variables compared to those used in Ref. 13, we red-
erive the ray-tracing equations for quasi-longitudinal and
quasi-transverse waves suitable for a-channeling. Nu-
merical simulations of a-channeling in a mirror machine
*Electronic address: firstname.lastname@example.org
tElectronic address: email@example.com
outlined in Ref. 14 supported the feasibility of using a-
channeling concept proposed in Refs. 12 and 15 in prac-
tical open-ended devices. A rough optimization of a-
channeling efficiency with respect to rf region parameters
(not constrained by the plasma dispersion relation) was
also presented in Ref. 14. In a subsequent study , the
search for the weakly-damped localized modes in plas-
mas was addressed and two distinct waves suitable for
a-channeling were identified in two practical mirror de-
vices [16, 17]. The method of the wave search used in
Ref. 13 is rederived here using a more convenient set of
coordinates matching the topology of the magnetic field
lines and lines orthogonal to them.
The paper is organized as follows. In Sec. II, we
discuss the a-channeling concept and its application to
open-ended devices. In Sec. III, previous results con-
cerning the optimization of the a-channeling efficiency
with respect to rf region parameters are discussed. In
Sec. IV, we discuss how the search for the waves suit-
able for a-channeling can be conducted. We rederive the
ray-tracing equations for the quasi-longitudinal and the
quasi-transverse waves using canonical curvilinear coor-
dinates and then use these results to formulate a method
suitable for identifying spatially localized weakly-damped
modes. In Sec. V, we discuss the modes suitable for a-
channeling identified in two practical open-ended designs
[16, 17] and in the LAPD device . Section VI sum-
marizes our conclusions.
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Zhmoginov, A. I. & Fisch, N. J. Feasibility Studies of Alpha-Channeling in Mirror Machines, report, March 19, 2010; Princeton, New Jersey. (https://digital.library.unt.edu/ark:/67531/metadc1013916/m1/3/: accessed March 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.