From: Long-Poe Ku [lpku@pppl.gov]
Sent: Monday, August 06, 2001 1:25 PM
To: Mike Zarnstorff; Wayne Reiersen
Cc: Dennis Strickler
Subject: Optimized S3 for M12 and M21

Mike, Wayne;

Comparsions of some physics properties at the S3 state for the smoothed M12
(0227) coil and for the more recently developed M21 (0711) coil are given
below.  M21 is an 18 coil design having coils on neither v=0 nor v=1/2
symmetry planes. It is a case of having one of the lowest Bmax error in
coilopt.  In each case, results of the best state obtained so far, after
optimizing coil currents,  are shown.  We, of course, assume that good flux
surfaces exist throughout the entire plasma region.

Long-Poe Ku



A) M12 --  smoothed coil (0227a2): M12K52; without smoothing (0227a1): M12K29

A.1. MHD stability

	-- Both are essentially stable to the external kinks with 91
displacement modes. Both are slightly unstable to ballooning at 4.1% beta
near the boundary in narrow regions, as the baseline (fixed boundary)
plasma.

A.2. QA

	-- The effective ripples of M12K52 are slightly higher than those
of M12K29. Both are higher in the core and lower in outside regions than
the baseline. The effective ripples calculated by NEO at r/a~0.5 are 0.21%,
0.27% and 0.28% for the baseline, M12K29 and M12K52, respectively. At
r/a~0.7, the effective ripples are 0.68%, 0.60% and 0.65%, respectively,
for the three cases.

	-- For energetic ions, the NBI particle slowing down calculations,
using the model profiles, show an average energy loss fraction of 14.4%,
13.7%, and 14.9% for the baseline, M12K29 and M12K52, respectively.  Here,
the calculations are for 1.7 m machine at 2 T.  The injected species is
hydrogen, and the injection energy is 40 keV.  The average loss fraction
quoted above is the unweighted average of neutrals deposited initially at
toroidal angles 0, 90 and 180 degrees with tangency radius equal to the
magnetic axis.

A.3. Coil currents

	-- The smoothing of bend radii causes increase in current in
modular coil #3 and decrease in coil #4 in order to achieve the optimized
state in terms of physics quatities. The current ratios relative to the
original coilopt design are 1.030, 1.0185, 1.024 and 1.042 for the M12K29
modulars, and 1.040, 1.018, 1.054 and 1.017 for the M12K52 modulars. The
ratios for the 1/R field are 0.95 and 0.93 for M12K29 and M12K52,
respectively.

B) M21 -- M21.3.K17

B.1. MHD stability

	-- M21.3.K17 is stable both to the kinks and ballooning at 4.1%
beta within the present calculational resolution for our routine
assessments. The external kink stability is quite marginal in that a slight
change in equilibrium may cause the plasma to go marginally unstable.

B.2. QA

	-- The effective ripples are 0.33% and 0.63%, respectively, at
r/a~0.5 and 0.7. The ripple in the core clearly is higher than M12K52
(0.28%), but it is considerable lower than that of the other 18 coil
designs.  Indeed, it compares favorably with most 21 coil designs with a
symmetry coil at v=0, which usually give better QA. We note that, without
current optimization, the reconstructed plasma still has a mirror field of
about 0.35% penetrating all the way to the center.  The optimization is
such that the mirror field is pared down substantially and at the same time
the plasma is made more stable to MHD modes.

	-- For NBI particles, the average energy loss fraction is 13.9%.
This is to compare to 14.4 % of the baseline plasma and 18.5% of the
"as-designed" plasma (i.e. before the otpimzation to reduce the mirror
field).

C) Coil currents

	-- There are substantial modifications of coil currents in the
vertical field coils as a result of the optimization of the physics
parameters. The current ratios of VF coils relative to the coilopt design
are -0.09, 2.37, 0.07, 4.78, -6.61, respectively, for VF1 to VF5. Of these,
VF2 has a current 1.06 MA for a 1.4m major radius machine.  In the original
design, fields are provided mostly from VF1, VF2 and VF3.  In the physics
optimized case, fields are provided mostly from VF2 and VF4. We did not,
however, turn on coil current regularization in the optimization.  The
changes in modular and 1/R field are more modest. The current ratios are
1.016, 1.019, 1.036 for the modulars, and 0.925 for the 1/R.