Particle and energy exchange between untrapped and electrostatically confined populations in magnetic mirrors

Abstract

The effect of passing particles on the confinement of particles trapped in a magnetic mirror with confining electrostatic potential is examined. Exact relations between the particle and energy fluxes and the distribution functions for two auxiliary boundary value problems are derived. Approximate analytic expressions for these fluxes, asymptotically valid for large ratio of confining potential energy to trapped-particle temperature and either large or small mirror ratio, are obtained. The results are applied to the determination of the ambipolar potential and the temperature difference between trapped and untrapped electrons in a stream-stabilized conventional mirror machine such as 2XIIB and in the plug cells of a tandemmirror machine. An important result is that, under a wide range of conditions, the potential difference Φ between the plug and the barrier of a thermal-barrier tandem-mirror machine is given by eΦ = Tep ln [(np/nb) (Tec/Tep)1/2], a modification of the Maxwell-Boltzmann result.

Thermal Barrier Formation and Plasma Confinement in the Axisymmetrized Tandem Mirror GAMMA 10

“…All of these results are consistent with the thermal-barrier concept. 5 The barrierpotential depression of 100-300 V agrees within a factor of 2 with theoretical prediction 15,16 for the centralcell T ec in the range of 60-120 eV. ELA's cannot be used for plug-potential measurement for the case of too-strong plugging because of such small ion-end-loss fluxes.…”

Chemical Kinetics of Chlorine in Electron Cyclotron Resonance Plasma Etching of Si

“…(9) models the power lost when an electron from neutralbeam ionization, born at essentially zero energy, heats to 0 b + 0 C parallel energy and becomes a passing electron, carrying an average perpendicular energy of T ep along. The last term is the energy transfer between plug electrons and central-cell electrons which surmount the thermal barrier and enter the plug [17]. These equations are used in conjunction with power balance equations for central-cell ions and electrons, hot electrons in the thermal barrier, and the energy input by charge-exchange pumping in the thermal barrier.…”

Mirror fusion. Quarterly report, October-December 1980

“…In its simplest form, the BAAL algorithm is derived by linearization of the particle positions relative to (0) xn+I• One can regard the actual position xn+ 1 as x~~~ plus a displacement ox = (J~t 2 an+ 1 . We form the charge density p~~~ from 1<~1}; the actual charge distribution is then p ~~I' plus the change op brought about the displacing particles by the amount ox (29) To the same order of approximation, the displacement ox{x) of all particles with X ~~I~ X is obtained with an+ 1 evaluated at x; i.e., (30) We then have…”

“…The field -' i7 <'~>n+ 1 and Eq. (30) are then used to calculate the positions lxn+ tl• This algorithm i~re{lli'niscent of the method for solution for the /v~ctor"'-potential A in some magnetoinductive plasma si'mulations~odes. 14 -16 Should it be necessary, we have shown how to refine the approximations used above by linearization about a more accurate prediction of xn+ 1 than…”