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# Ball-Pen probe diagnostic
## Objectives
The final aim of the experiment will be to improve our understanding of the Ball-Pen probe and its benefits in the measurements in magnetized plasmas.
## Description
The usual way to calculate the plasma potential inside the GOLEM is by using Langmuir probes. The probe measures the floating potential $U_{fl}$ but we can find the plasma potential $\Phi$ using the next equation:
$$U_{fl}=\Phi+T_e\ln(R)$$
Where $R=\frac{I_{sat}^-}{I_{sat}^+}$ is the ratio between the saturation currents for electrons and ions.
The [Ball-Pen probe](https://en.wikipedia.org/wiki/Ball-pen_probe). was developed in the tokamak GOLEM [1] to improve the measurement of the plasma potential in the reactor. Basically, it is a Langmuir probe with a movable shield, this shield can moderate the incidence of electrons into the probe taking advantage of the Larmor radii [4], changing the value of $R$.
The [Ball-Pen probe](https://en.wikipedia.org/wiki/Ball-pen_probe) was developed in the tokamak GOLEM [1] to improve the measurement of the plasma potential in the reactor. Basically, it is a Langmuir probe with a movable shield, this shield can moderate the incidence of electrons into the probe taking advantage of the Larmor radii [4], changing the value of $R$.
This theory is not completely satisfactory because some research [1][2] has shown that there is always electron current in the probe, also when the probe is deep inside the shield which is in contradiction with the theory. It was found that the E × B drift motion of electrons moving along the equipotential surface plays an essential role in the measurement [7]. To solve this problem, it has been proposed that the shield have the same potential as the probe collector itself.
This theory is not completely satisfactory because some research [1][2] has shown that there is always electron current in the probe, also when the probe is deep inside the shield which is in contradiction with the theory. It was found that the $E\times B$ drift motion of electrons moving along the equipotential surface plays an essential role in the measurement [7]. To solve this problem, it has been proposed that the shield have the same potential as the probe collector itself.
## Methodology
The experiment will consist in measurement of the I-V characteristic curves for different positions of the probe inside the shield, the saturation line will give us the parameter $R$. Once the parameter $R$ is close to 1 then we have reached the desired position $h$.
The experiment will consist in measurement of the $I-V$ characteristic curves for different positions of the probe inside the shield, the saturation line will give us the parameter $R$. Once the parameter $R$ is close to 1 then we have reached the desired position $h$.
Know this distance $h$ has great importance because it can be used in future experiments to improve the measure of the plasma potential.
## Bibliography
[1] J. Adámek et al, _A novel approach to direct measurement of the plasma potential_
[2] J. Adámek et al, _Comparative measurements of the plasma potential with the ball-pen and emissive probes on the CASTOR tokamak_
[3] R. Schrittwieser, C. Ionita, _Direct measurements of the plasma potential by katsumata–type probes_
[4] Itsuo Katsumata and Moroe Okazaki, _Ion Sensitive Probe-A New Diagnostic Method for Plasma in Magnetic Fields_
[5] J. Adámek et al, _Simultaneous Measurements of Ion Temperature by Segmented Tunnel and Katsumata Probe_
[6] Jana Brotánková, _Study of high temperature plasma in tokamak-like experimental devices_
[7] N. Ezumi, _PIC Simulation of the Motion of Plasma around Ion Sensitive Probes_
[8] Robert L. Merlino, _Understanding Langmuir probe current-voltage characteristics_
