Effect of temperature gradients on neoclassical scaling of tandem mirror transport

Abstract

A one-dimensional radial model for tandem mirror transport is developed for the study of the effect of temperature gradients. Induced azimuthal electric fields are neglected for simplicity. In the limit of large collisional energy exchange between electrons and ions -often appropriate to present-day tandem mirror experiments -the confinement time scaling law 7j _ ~ (A<J>)~3 /2 is obtained for TMX-U.

Neoclassical resonant plateau transport calculation in an effectively axisymmetrized tandem mirror with finite endplate resistance

“…A (r) increases radially with r. A similarly flat profile has been obtained in Ref. [18]; this result is in contrast to the case where the potential profile is assumed to be parabolic and r^A(r) is roughly proportional to r" 2 [8]. The result for small R stems from the fact that e$(r)/T e (r) is radially almost constant, and so is the electron axial loss, according to Pastukhov scaling.…”

“…The electrostatic potential, $(r), is determined from the charge neutrality equations, Here, T t is the ion radial loss, F e is the electron axial loss, L hs = L s /2, and T^ is the Pastukhov confinement time [16,17]. The regularity condition at r = 0 requires finite Larmor radius corrections to Dj for j = 0, 1 such that Dj(r) = (r 2 + 5 2 ) Dj(r = 1 cm) with 6 = 0.5 cm [9,18]. The boundary condition for 4»(r) at the wall is given by *c,,d = R X I, iet er e (r).…”

“…11) with self-consistent potential included; dashed and broken lines are calculated from Eq. (18). Dashed lines: L Tl = oo; broken lines: L Tl = 20 cm.…”

The magnetic mirror approach to fusion

“…Other factors, such as radial variations in the electron temperature, may also influence the transport. In an effort to explore such effects, Myra et al [236] have investigated the effect of temperature gradients on transport. Using a one-dimensional radial model employing Clebsch co-ordinates and an assumed radial profile of T e , Myra et al find a 0" 3/2 dependence of the radial confinement time.…”

Radial transport in a tandem mirror

“…(l). Even so, a more selfconsistent calculation 16 including the effect of asymmetric heating is preferred.…”