Paleoclassical plasma transport in toroidal plasmas*

J.D. Callen, University of Wisconsin, Madison, WI 53706-1609 USA

   Plasma transport in tokamaks has generally been considered to be "anomalous" ever
 since the pioneering Russian T-3a experiments in the late 1960s. Most prominently, radial
 electron heat transport usually exceeds (by factors of a hundred or more) 
Coulomb-collision-induced transport via the oscillatory radial motion of charged particles
 gyrating (classical) and drifting (neoclassical) in magnetized toroidal plasmas.
 Many mysterious characteristics of electron heat transport have been uncovered over the past
 four decades -- transport typically a multiple of the magnetic field diffusivity in ohmic plasmas, confinement 
scaling with the electron density in high density plasmas (Alcator scaling), heat pinches, 
internal transport barriers around low order rational surfaces (in RTP), incremental and 
transient transport usually exceeding "equilibrium" transport, etc.

   A "paleoclassical" transport model has recently been introduced* to explain 
the "anomalous" transport in ohmic-level tokamak plasmas. The basic hypothesis 
of the paleoclassical model is that the guiding centers of charged particles 
are attached to and diffuse radially along with thin annuli of poloidal magnetic 
flux on the magnetic field diffusion time scale. This hypothesis has recently been
derived* by transforming the drift-kinetic equation from laboratory coordinates to 
poloidal magnetic flux coordinates in resistive, current-carrying axisymmetric toroidal plasmas (e.g., tokamak
plasmas) where the poloidal flux obeys a diffusion equation. The amount of 
electron heat transported radially by this process is a multiple of the magnetic 
field diffusivity that represents how far (relative to the poloidal periodicity field 
line length) parallel electron heat conduction equilibrates the electron temperature 
along field lines -- the minimum of the electron collision length, an electromagnetic 
skin depth-determined length, or the length of field lines on and near low order 
rational surfaces. The resultant radial electron heat transport is called "paleoclassical" 
since it results from a combination of two very primitive processes that have been known 
for a long time: radial magnetic field diffusion due to plasma resistivity and parallel 
electron heat conduction.

   Predictions of the paleoclassical transport model have been
compared* with data from many toroidal plasma experiments: electron heat 
diffusivity in DIII-D, C-Mod and NSTX ohmic and near-ohmic plasmas; transport 
modeling of DIII-D ohmic-level discharges and of the RTP ECH "stair-step" experiments 
with eITBs at low order rational surfaces; investigation of a strong eITB in JT-60U; 
H-mode T_e edge pedestal properties in DIII-D; and electron heat diffusivities in 
non-tokamak experiments (NSTX/ST, MST/RFP, SSPX/spheromak). The radial electron 
heat transport predicted by the paleoclassical model is found to be in reasonable 
agreement with a wide variety of ohmic-level experimental results and to set the 
lower limit (within a factor ~ 2 in tokamaks) on the radial electron heat transport 
in most resistive, current-carrying toroidal plasmas -- for T_e < T_e^{crit} ~ B^{2/3} a^{1/2} keV 
where it is expected to be dominant over microturbulence-induced transport that 
scales with a gyro-Bohm-level diffusion coefficient. Some of these comparisons will be highlighted. 
Also, additional plasma transport processes that result from the paleoclassical 
model will be noted -- density, ion heat and toroidal flow transport, all with pinch-type effects.


* For published papers and reports on the paleoclassical model and 
experimental tests of it see http://homepages.cae.wisc.edu/~callen .