TJ-II:Heavy Ion Beam Probe: Difference between revisions

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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


<center><math>
:<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></center>
</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


<center><math>
:<math>
\phi(B) = 2\phi_{ana}( F\delta i + G ) - \phi_{inj}~.
\phi(B) = 2\phi_{ana}( F\delta i + G ) - \phi_{inj}~.
</math></center>
</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  


<center><math>
:<math>
0 = 2\phi_{ana}(F\delta i_0 + G) - \phi_{inj}~.
0 = 2\phi_{ana}(F\delta i_0 + G) - \phi_{inj}~.
</math></center>
</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


<center><math>
:<math>
\phi(B) = 2\phi_{ana} F(\delta i - \delta i_0)~.
\phi(B) = 2\phi_{ana} F(\delta i - \delta i_0)~.
</math></center>
</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


<center><math>
:<math>
i = i_u + i_d \propto n_e(B)~.
i = i_u + i_d \propto n_e(B)~.
</math></center>
</math>


== Data Analysis Tools ==
== Data Analysis Tools ==

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