Measurement of Magnetic Null and Field Reversal in FRC Plasmas using the Hanle Effect
P. 1

! Motivation and Summary
•  Main contribution to fusion energy release comes from the
suprathermal “tails” of the distribution functions of the fusing ions
•  At these higher energies, the ion Coulomb collision rates become much lower than for the thermal ions, and deviation of the ions from the Maxwellian becomes substantial
•  A kinetic analysis of the ion distributions for suprathermal energies becomes necessary for a reliable evaluation of the fusion reactivity
•  We develop a convenient tool for such analysis, focusing on the p11B systems
•  We identify several favorable effects leading to improved energetics of the system
!  Outline
!  Reactingparticlesenergylossandrecovery
!  Distributionfunctionofreactingparticlesinp11Bplasmaand potential for increasing the fusion yield
!  Kineticequationforhigh-energyprotons
!  Summary and future work
Appendix 1: Ion cooling by electron drag
Appendix 2: Suppression of the relativistic electron tail
! Evaluation of the average energy of reacting particles
Each fusion reaction leads to a removal of particles and energy from the fusing ions. In the case of the p11B plasma the reaction products are charged particles that stay in the plasma, leading to almost complete recovery of the energy loss
There exist accurate expressions for the fusion power without an account for the energy of fusing particles,
e.g. NRL Plasma Formularly for DT and 2000 Nevins and Swain for p11B.
One can show that the average energy of the ions contributing to fusion reaction is
This energy is split between the reacting ions as
For p11B fusion, 11/12 of energy comes from hydrogen
! Developing the kinetic description for the protons in a fusion-relevant pB11
The proton distribution function at the energies ~ 1MeV is affected by a number of processes:
-  Interaction with the thermal protons and Borons (dynamic friction and diffusion)
-  Interaction with sub-relativistic electrons -  Interaction with the slowing-down alphas -  Fusion burn-out
-  Particle injection
What makes this problem manageable:
-  Distributions are almost isotropic due to the presence of Borons and alphas
-  Collisions between fast protons can be neglected
-  Electrons, borons and thermal protons have Maxwellian
The kinetic equation for the “tail” ions reads as:
Using the standard formalism of the Coulomb collisions and dynamic friction coefficients for the protons on protons, borons, and electrons from the detailed balance principle. For the electrons non-relativistic expression are used that leads to ~ 10 % error (D. Barnes)
Allphas are non-Maxwellian and require separate treatment
16π2ΛZα2e4v2 ∞∫ ( ) Dα= 3m2 vʹfα vʹdvʹ
p v0
We evaluate the relative significance of various processes for the set
of possible parameters of future p11B reactor:
Tp=TB=350keV, Te=150 keV, np=1.5⋅1014 cm-3, nB=0.15nP, ne=2np,
For this set of parameters we have:
DB /Dp =0.38; De /Dp =0.37; Dα /DP =0.5
In other words, a correct accounting for all types of collisions is
One can check that, in the dynamic friction terms, the role of alphas is negligible. The relative (with respect to protons) contributions of
other collisions to dynamic friction is 1 for the Borons and (T/Te)(De/ Dp) for the electrons
The ratio of the dynamic friction and the diffusive terms in our kinetic equation determines an “effective temperature” that the suprathermal protons would have had without any losses or sources
Cooling down on the electrons is fully compensated by the alpha- heating
The proton distribution function in the range of 1 MeV is distorted Maxwellian due to the presence of sources and sinks
!  Redline:NBIsource,Blue:fusionsink,Reddashanticipated change of the tail
!  Summary
!  A tool for the analysis of the proton distribution function has been
!  Diffusion coefficients and dynamic friction against all the components have been quantitatively evaluated.
!  An increase of the fusing ion population is linked to the particle flux in the velocity space that compensates for the particle loss from the bulk plasma
!  The system has a potential for improved performance via optimization of the energy distribution of the injected protons (future work)
! References
W.M Nevins. JOFE, 17, 25 (1998)
W.M. Nevins and R. Swain. NF, 40, 865 (2000) B.A. Trubnikov. In: Reviews of Plasma Theory, v. 1, Plenum, 1965
Two fusing particles, say, p and
enter a collision with the energies m1v12/2 and m2v22/2 . The fusion energy release in the reaction is Ef.. Therefore, the energy of the reaction products (three alpha-particles in the case of a p11B) will be
For the ion temperature of 250-400 keV, the average energy of the reacting particles is 1-1.2 MeV. The total energy of the just born alphas is, accordingly, not 8.7 MeV, but rather 9.7 - 9.9 MeV
The same effect exists in the DT reactions
B (particles “1” and particle “2”)
Energy spectrum and kinetics of the fusing particles D.D. Ryutov, S.V. Putvinski, P.N. Yushmanov, and the TAE Team
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
2 T(100keV)
!  Here, however, 80% of the thermal energy contribution leaves the plasma in the form of neutrons and is recovered with the lower (thermal) efficiency
! Conclusions:
!  Reacting protons are suprathermal, their collision frequencies are low, and their distribution function may deviate from the Maxwellian; we need a kinetic description of the ion “tails”
!  Thisopensupapotentialpossibilityofproducing“engineered” distribution function of the suprathermal ions and increasing the fusion reactivity
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