## Linear Growth Rates for D3D shot 81499 at 4.000 secs

Here are the gyrofluid linear growth rates for D3D shot 81499 at 4.000
secs and rho=0.5. These results are still using circular concentric flux surfaces,
but show the effect of including Ti/Te, impurities, and trapped electrons.
I am again using Lang Lao's profiles for the input parameters.
Also note that rho_i=sqrt(T_i/m_i)/Omega_i, without the sqrt(2).

First, with adiabatic electrons:

Neglecting impurities but including the measured Ti/Te drops the growth rates from the solid line with
closed circles to the dashed line with open circles, both with
adiabatic electrons. The dashed line with open circles
corresponds to the case I sent last week, which used the measured Ti/Te. If I then include impurities (D+C+beams),
rho=0.5 is essentially marginally stable:
I find a VERY weak instability for k_theta rho_i=0.3, and all other k_theta's are
damped, so I didn't put this curve on the graph. In this parameter regime
my growth rates are slightly low: I'd expect a peak gamma around 0.05-0.1 x 10^5 1/s from
a fully kinetic calculation with impurities using the measured Ti/Te.

Adding trapped electrons and including impurities and Ti/Te brings the growth rates
back up from zero, as shown with the solid line and open squares. With trapped
electrons, this is still an ITG mode: the real frequencies change very slightly.
I should mention that I haven't double checked my calculation of the electron
collisionality when using D3D input data, so the growth rates with trapped electrons might
change slightly. Does nu_*e=0.1 sound about right, Lang?

The conclusion from this exercise is that (at rho=0.5) this shot is close to
marginality to the ITG mode. Trapped electrons will change the threshold
somewhat, as will changes in the impurity and beam densities and gradients.

I think rho=0.5 in circular concentric geometry with Ti=Te and no impurities
would be a good place to do a nonlinear comparison, once we get agreement
with these growth rates (the solid line with closed circles).

--Mike.

P.S.
Lang: in the file D814994000prof, the last grid point (51) doesn't satisfy quasineutrality.
(?)

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