Collisional loss of electrostatically confined species in a magnetic mirror

Abstract

The basic problem of particle end-loss in a magnetic mirror field with an electrostatic confining potential is considered. The analytic treatments of Pastukhov and Chernin and Rosenbluth have been generalized to apply to any electrostatically confined species in a multi-species plasma, and the Pastukhov analysis has been extended to apply to arbitrary magnetic-field profiles (instead of square-well). The analytic results are compared with results obtained from one-and two-dimensional Fokker-Planck codes. In particular the scaling with potential, mirror ratio, and effective charge is considered. The closest agreement (within 20%) is between the 2-D Fokker-Planck and generalized Pastukhov results.

Generalized Scaling Laws of the Formation and Effects of Plasma-Confining Potentials for Tandem-Mirror Operations in GAMMA 10

“…(2) and (3) along with the generalized Pastukhov theory for the confinement of the central-cell bulk electrons. (The results from various modifications of Pastukhov's theory [9,20,21] range in the present data plots within the error bar. )…”

“…Even at this time, however, the physics-mechanism and scaling studies on the basis of the comparison between experimental data and potential theories [6][7][8][9] are reported in a limited number of publications for specific plasma operations alone [10][11][12].…”

“…These data summaries are physically interpreted, combined, and then generalized under the proposed consolidation and combination of the two major theories of Cohen's strong electron-cyclotron heating (ECH) theory [6] and generalized Pastukhov's potential confinement theory [8,9] by the use of electron-energy and particle balance equations.…”

“…The dashed curves are simulated from Eq. (3) with Pastukhov's particle-confinement time [8,9] into t p . The tendency of an increasing neutralshielding effect with increasing T e or f b is seen by the data from f b ഠ 0.8, through 0.5, and then to 0.2 kV, since these data are traced by the dashed curves labeled 1 and 2 (corresponding to n 0 1, and 2 3 10 15 m 23 , respectively), and then the calculations with poorer shielding with n 0 ഠ 5 3 10 15 m 23 , respectively.…”

Measurements of radial profiles of ion cyclotron resonance heating on the Tandem Mirror Experiment-Upgrade

“…For ease of calculation, one can assume the particle has its guiding center on the 2-axis so r is equal to the gyroradius, p. Substituting this into the expression for the force yields: qp 8B Z mv ± 2 dB z dB z F * = -Y v±~t e = -"SB" aT = ~M"^ (2 " 7) where the quantity (mv 1 2 )/(2B) is identified as the magnetic moment, p..…”