DNB Attenuation or

1
DNB AttenuationorMisuse of MSE
Datacontinued
MIT Plasma Science and Fusion Center

• Rachael McDermott, Bill Rowan
• Thanks to Steve Scott and Howard Yuh
• for numerous consultations

2
What and Why?

• Using MSE data to find accurate estimates of
  neutral beam attenuation
• These measurements can be used to benchmark beam
  penetration codes currently in use.
• Accurate knowledge of neutral density is
  necessary for calculations of impurity densities
  in the plasma.

3
Last time we

• Found a set of channel-to-channel calibration
  factors for the MSE diagnostic
• Used these factors to derive relative beam
  attenuations from the MSE signal for beam into
  plasma shots

To Do List from last time

• Understand the calibration at all pressures.
• Compare the attenuations to standard results
  from the literature and from our own penetration
  code

4
Calibration Constants
Shot 002 003 004 005 006
Pressure (mT) 2.45 1.215 .5939 .5903 .2697
Channel (m)
.86786 1.00000     1.00000   1.00000    1.00000   1.00000
.85243 0.352164   0.58445     0.717148   0.708050 0.803426
.83575 0.196582    0.55356     0.949377   0.92907     1.23440
.81979 0.039039   0.19822     0.42616     0.414802 0.605755
.78509 0.00438422 0.0736256   0.288886   0.283944  0.542222
.76645  0.00151599  0.0490210    0.260984   0.249218  0.551441
.74647 0.000307003   0.0191607   0.143248   0.133928 0.321710
.72641 0.000171313  0.0213610    0.24522    0.230223  0.664743
.70109 2.73887e-05  0.00777271   0.127916   0.112520 0.347466
.67594 5.02186e-06 0.00373183  0.086171  0.0745174  0.222317

• Due to a calculation error, the calibration
  constants presented at the last presentation were
  incorrect. The correct (hopefully) constants are
  shown above.
• We still dont have an explanation for the
  discrepancies between the pressures. The lowest
  pressure constants are used for the beam density
  calculation.

5
Comparison to Literature

• An analytical fit to the stopping cross-section
  for a neutral beam into a hydrogen plasma as
  derived by Janev is
• A theoretical beam attenuation can be derived
  from this as follows

Janev, R.K., Boley, C.D., Post, D.E. (1989)
PENETRATION OF ENERGETIC NEUTRAL BEAMS INTO
FUSION PLASMAS. NUCLEAR FUSION, Vol. 29, No.12,
2125-2139
6
Decay Constants

• All of the attenuation curves were fit to
  The
  values of the parameters for two shots are given
  in the table below.
• As the level of impurities is increased in the
  predicted model so does its agreement with the
  MSE attenuation.

Shot   MSE No Impurities 1C 2C
1040409007 a -0.036409910 -0.078569204  0.071894864 -0.067443145
1040409007 ß  1.1521804     1.1679132   1.1600576   1.1541364
1040409007 ? 0.12570610 0.16726451  0.16841049  0.17047122
1040505029 a -0.13186031    -0.1694330    -0.16218624  0.15475712
1040505029 ß   1.3511533     1.4181084 1.4075826   1.3967821
1040505029 ? 0.15018593  0.13794946 0.13883806 0.13977914
7
Prediction and Experiment
The predicted beam attenuation for each shot is
calculated using the CMOD temperature, and
density profiles. The temperature profile was
obtained from ECE. The density profile was
obtained from the Visible Bremsstrahlung
diagnostic.

• An MSE derived beam attenuation along with its
  corresponding Janev-predicted beam attenuation is
  pictured above. This is for shot 1040505029.

8
Conclusions

• An astonishing 39 of 41 shots fit well to
  exponential curves and were consistent with
  predicted results.

To Do List

• Explain calibration constant variation with
  pressure. Find another way to derive a
  channel-to-channel MSE calibration.
• Include an error analysis in the derivation of
  the densities.
• Include a measure of the difference between the
  calculated and predicted attenuations.
• Finish writing this program in a user friendly
  form that can be run after each shot.