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TJ-II:Heavy Ion Beam Probe: Difference between revisions
→Operational expression for the electric potential \phi
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The energy analyser of the HIBP diagnostic at TJ-II is of the Proca-Green type. The kinetic energy of the secondary ions entering the analyser is given by | The energy analyser of the HIBP diagnostic at TJ-II is of the Proca-Green type. The kinetic energy of the secondary ions entering the analyser is given by | ||
:<math> | |||
E_k = q'\phi_{ana}(F\delta i + G)~, \quad \delta i = \frac{i_u - i_d}{i_u + i_d}~, | E_k = q'\phi_{ana}(F\delta i + G)~, \quad \delta i = \frac{i_u - i_d}{i_u + i_d}~, | ||
</math | </math> | ||
where <math>\phi_{ana}</math> is the deflecting electric potential in the analyser gird, <math>i_{(u,d)}</math> are the currents measured on the up and down plates of the analyser and <math>F</math> and <math>G</math> are adimensional geometric factors depending on construction parameters and on the entrance angle of the ions entering the analyser. The kinetic energy of the ions at the injection point <math>E_{k,A}</math> can be written as their charge times the accelerating potential in the injector, i.e., <math>E_{k,A} = q\phi_{inj}</math> | where <math>\phi_{ana}</math> is the deflecting electric potential in the analyser gird, <math>i_{(u,d)}</math> are the currents measured on the up and down plates of the analyser and <math>F</math> and <math>G</math> are adimensional geometric factors depending on construction parameters and on the entrance angle of the ions entering the analyser. The kinetic energy of the ions at the injection point <math>E_{k,A}</math> can be written as their charge times the accelerating potential in the injector, i.e., <math>E_{k,A} = q\phi_{inj}</math> | ||
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Substituting this and the Proca-green expression for the enery into the formula for the electtric potential and inserting, for the particular case of TJ-II, <math>q'(\textrm{Cs}^{2+}) = 2</math> y <math>q(\textrm{Cs}^+) = 1</math>, one gets | Substituting this and the Proca-green expression for the enery into the formula for the electtric potential and inserting, for the particular case of TJ-II, <math>q'(\textrm{Cs}^{2+}) = 2</math> y <math>q(\textrm{Cs}^+) = 1</math>, one gets | ||
:<math> | |||
\phi(B) = 2\phi_{ana}( F\delta i + G ) - \phi_{inj}~. | \phi(B) = 2\phi_{ana}( F\delta i + G ) - \phi_{inj}~. | ||
</math | </math> | ||
In a stellarator it is possible to calibrate the measurement of the plasma electric potential. After the end of the plasma discharge but still during the flat-top of the machine currents the injection of a short pulse of neutral gas provides a zero-potential signal | In a stellarator it is possible to calibrate the measurement of the plasma electric potential. After the end of the plasma discharge but still during the flat-top of the machine currents the injection of a short pulse of neutral gas provides a zero-potential signal | ||
:<math> | |||
0 = 2\phi_{ana}(F\delta i_0 + G) - \phi_{inj}~. | 0 = 2\phi_{ana}(F\delta i_0 + G) - \phi_{inj}~. | ||
</math | </math> | ||
Subtracting the above equations a simplified expression for the electric potential is obtained | Subtracting the above equations a simplified expression for the electric potential is obtained | ||
:<math> | |||
\phi(B) = 2\phi_{ana} F(\delta i - \delta i_0)~. | \phi(B) = 2\phi_{ana} F(\delta i - \delta i_0)~. | ||
</math | </math> | ||
The ionization rate of primary ions in a plasma volume is approximately proportional to the local electron density. For the high energy neutral beam and the low density plasmas, as found in the TJ-II device, the attenuation of the secondary beam along its trajectory from the ionization or sample volume to the analyser is negligible. In this situation, the total current on the analyser plates <math>i = i_u+i_d</math> is approximately proportional to the electron density in the sample volume | The ionization rate of primary ions in a plasma volume is approximately proportional to the local electron density. For the high energy neutral beam and the low density plasmas, as found in the TJ-II device, the attenuation of the secondary beam along its trajectory from the ionization or sample volume to the analyser is negligible. In this situation, the total current on the analyser plates <math>i = i_u+i_d</math> is approximately proportional to the electron density in the sample volume | ||
:<math> | |||
i = i_u + i_d \propto n_e(B)~. | i = i_u + i_d \propto n_e(B)~. | ||
</math | </math> | ||
== Data Analysis Tools == | == Data Analysis Tools == | ||