Bruce D. Scott, Max Planck Institut fuer Plasmaphysik, EURATOM Association, D-85748 Garching, Germany
general result used in several presentations
An important quantitative result of low frequency electromagnetic ExB drift turbulence driven by background gradients is its scaling with the local pressure gradient. The parameter controlling this stems from a competition between interchange forcing and an electromagnetic parallel electron response. This response is called the adiabatic response, since it tends to force the state of adiabatic electrons (p_e = phi in normalised disturbances), which is the traditional name for a quasistatic parallel force balance between the pressure and electric forces. If the electrons are adiabatic there is no net transport because the velocity component up and down the gradient is out of phase with the pressure disturbance (the flow stream function is _in_ phase).
In a tokamak plasma, the salient parameter is given by
alpha_M = q^2 R |grad beta|
where beta gives the gas pressure/magnetic pressure ratio, R is the
major radius, and q is the field line pitch parameter (toroidal turns
for one poloidal turn). The scaling of the transport at constant
magnetic field and at constant collisionality is
shown here.
It is important to show this at constant B rather than, as is more
usual, constant rho_star (drift scale/pressure gradient scale ratio).
In that normalisation the transport falls lightly with alpha_M,
erroneously suggesting a situation where more heating of the plasma
yields less transport. When doing the scaling in normalised units, one
must multiply the result by a factor of alpha_M^(1/2) in order to un-do
the normalisation [if it were done at constant density the factor would
be alpha_M^(1/2) because the normalised units for the transport scale
like T^(3/2), where T is the temperature].
Diagnosis of the various electromagnetic effects is summarised here [DALFTI is the local fluid model with all effects: B Scott, Plasma Phys Contr Fusion 40 (1998) 823-826]. These results are shown in normalised units, showing the misleading lightly falling trend referred to above. Nominal refers to all terms kept in the equations. Linear and nonlinear magnetic flutter is the action of the _perturbed_ parallel gradient on the background profile and on the disturbances, respectively. The results show that the principal effect at lower beta is stabilisation by linear magnetic flutter, for the same reason as for linear modes (0-D slab model with no shear)... you get a compensating term in the phase shift which leads to a lower growth rate. Nonlinear magnetic flutter tends to cancel the linear flutter, giving you a result more like the case where the only electromagnetic effect kept is magnetic induction [the result you see in B Scott, Plasma Phys Contr Fusion 39 (1997) 1635-1668]. For the drift wave case the nonlinear flutter enters about the same place as ideal ballooning... for the ITG case it enters below ideal ballooning. A similar but undiagnosed result for an ITG case relevant to the hot core regions of the plasma is presented in a recent Phys Plasmas paper by Snyder and Hammett.