ABSTRACT

The processes leading to end loss of ions from a mirror machine are reviewed. These include breakdown of adiabaticity, scattering and energy drag by classical collisions, and scattering by unstable fluctuations. Described are the linear theory of those modes thought to be of significance in present and reactor-size plasmas, and those features known of their nonlinear saturation. CONTENTS

Phys. Rev.Linear stability analyses of mirror machines with loss-cone ion distributions indicate that current high-density machines are unstable to the drift-cyclotron loss-cone (DCLC) mode with broadband frequency and wave-number spectra. 1,2 With the assumption that the ions are lost in a transit time after scattering into the loss cone, a previous quasilinear treatment predicted the trapped-plasma lifetime to be a few axial bounce periods. 3 This picture has seemingly been contradicted by experiments, as narrow-band spectra and containment times of several hundred bounce periods have been observed. 4 ' 5 Added to this, when a cold-plasma stream is injected, the containment time increases several fold. 6 * 7In this note we show that with refinement the quasilinear picture is indeed consistent with experiment and provides a unified description both with and without plasma stream. The essential modification from past analysis is to observe Lett. 28, 662 (1972). 5 V. N. Oraevskii and R. Z. Sagdeev, Zh. Tek. Fiz. 32., 1291 (1962) [Sov. Phys. Tech. Phys. 7, 955 (1963)]; R. P. H. Chang and M. Porkolab, Phys. Fluids J3, 2766 (1970). 6 These high-frequency signals are detected by a small double probe which couples to the external circuit through a transformer. By checking the directivity and sensitivity we confirmed that the probe detects the electric field. The resonant decoupling which may occur at the plasma frequency is suppressed by choosing a small probe-wire size comparable to the Debye length. 7 A simple geometric analysis of the dispersion relations indicates that all electron-plasma waves distributed in k space participate in excitation of the parametric instability only when k a is along the beam and equals 2oo 0 /u. Therefore, the observed ion-acoustic wave is the most unstable mode. that mirror plasmas do not necessarily fill the entire containment region of phase space available to them, but can be peaked at pitch angles nearly perpendicular to the magnetic field. Confinement is then improved, both because the unconfined phase-space region is given by v L 2 < (2q^/M { +v n 2 )/(jR, -1), and so is reduced if v n 2 % 2q$M i~1 ( <1> is the ambipolar potential and R the mirror ratio), and because untrapped particles of small t>n at the midplane have a longer transit time. The peaked distribution is maintained by the dominant velocity-space transport processes: electron drag which alters only the particle speed, and turbulent diffusion which affects primarily the perpendicular velocity v ± . In such cases the scattering time of ion-ion collisions, leading to pitch-angle broadening, is much longer than the first two transport processes, hence ion scattering does not alter the sharply peaked nature of the distribution. If the plasma initially A quasilinear model is developed describing the time evolution of a mirror-confined plasma which is unstable to the drift-cyclotron loss-cone mode. Good correlation is obtained with experiments with and without an external stream of cold plasma. 1051

A heavy ion beam probe has been used to measure the plasma space potential profiles in the tokamak TEXT [Nucl. Fusion Technol. 1, 479 (1981)]. The Ohmic discharges studied were perturbed by externally produced resonant magnetic fields (an ergodic magnetic limiter or EML). Without these perturbations the plasma central potential is generally consistent with the value calculated from radial ion momentum balance, using experimental values of density and ion temperature and assuming a neoclassical poloidal rotation velocity. Exceptions to the agreement are found when operating with reduced plasma parameters. Possible reasons for this discrepancy are explored, in particular, the effects of intrinsic magnetic field fluctuations, and modifications to the self-consistent radial electric sheath. With the application of the EML fields the edge electric field and potential increase during periods of magnetic island overlap. A test particle calculation of electron transport shows increases in diffusivity also occur during periods of magnetic island overlap. These calculated changes in diffusivity are interpreted in terms of a stochastic layer width, which is itself used to predict a potential change for comparison with the experimental results.