Turbulent Lifetimes in Mirror Machines

Abstract

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

Magnetic fusion energy annual report, July 1975--September 1976

“…The magnitude of this current is consistent with the scaling and magnitude predicted by quasi-linear theory. 6 Figure 25 has a diagram of the analyzer in sim plified form. We designed it to satisfy the following criteria while it operates in an axial magnetic field:…”

Studies of a Straight Field Line Mirror with Emphasis on Fusion-Fission Hybrids

“…A finite plasma flow through the mirror ends can stabilize the drift cyclotron loss cone (DCLC) mode [18]. Pumping in the expanders could maintain the density within margins given by Eq.…”

Applying Alpha-Channeling to Mirror Machines

“…Keeping the operating wave in resonance with both α particles and tail ions imposes significant restrictions on plasma parameters suitable for the channeling effect. In particular, even weak variations of the dc magnetic field can lead to resonant interaction between the wave and the bulk fuel ions, resulting in strong damping and plasma pump-out [10,11].…”

“…Moreover, in different magnetic confinement devices, there are different specific deleterious effects of energy residing too long in the α particles or in the electrons. Similar to instability effects driven by α particles in the tokamak [7][8][9], mirror instabilities, likewise stimulated by the energy in the α particles, might also diminish confinement of the plasma [10][11][12][13].…”