Ball-pen probe

Design and calibration

A ball-pen probe consists of a conically shaped collector (non-magnetic stainless steel, tungsten, copper, molybdenum), which is shielded by an insulating tube (boron nitride, Alumina). The collector is fully shielded and the whole probe head is placed perpendicular to magnetic field lines.

When the collector slides within the shield, the ratio ${\displaystyle R}$ varies, and can be set to 1. The adequate retraction length strongly depends on the magnetic field's value. The collector retraction should be roughly below the ion's Larmor radius. Calibrating the proper position of the collector can be done in two different ways:

1. The ball-pen probe collector is biased by a low-frequency voltage that provides the I-V characteristics and obtain the saturation current of electrons and ions. The collector is then retracted until the I-V characteristics becomes symmetric. In this case, the ratio ${\displaystyle R}$ is close to unity, though not exactly. If the probe is retracted deeper, the I-V characteristics remain symmetric.
2. The ball-pen probe collector potential is left floating, and the collector is retracted until its potential saturates. The resulting potential is above the Langmuir probe potential.

Electron temperature measurements

Using two measurements of the plasma potential with probes whose coefficient ${\displaystyle \alpha }$ differ, it is possible to retrieve the electron temperature passively (without any input voltage or current). Using a Langmuir probe (with a non-negligible) and a ball-point probe (whose associated ${\displaystyle R}$ is close to zero) the electron temperature is given by:

${\displaystyle T_e=\frac{\mathrm{\Phi }-V_{fl}}{\alpha }}$

where ${\displaystyle \mathrm{\Phi }}$ is measured by the ball-pen probe, ${\displaystyle V_{fl}}$ by the standard Langmuir probe, and ${\displaystyle \alpha }$ is given by the Langmuir probe geometry, plasma gas composition, the magnetic field, and other minor factors (secondary electron emission, sheath expansion, etc.). It can be calculated theoretically, its value being about 3 for a non-magnetized hydrogen plasma.

In practice, the ratio ${\displaystyle R}$ for the ball-pen probe is not exactly equal to one, so that the coefficient ${\displaystyle \alpha }$ must be corrected by an empirical value for ${\displaystyle R}$:

${\displaystyle T_e=\frac{{\mathrm{\Phi }}_{BPP}-V_{fl}}{\overline{\alpha }},}$

where ${\displaystyle \overline{\alpha }=\alpha -ln(R).}$

Ion temperature measurements

The ion temperature ${\displaystyle T_i}$ is an important quantity in fusion plasmas; however, it is only rarely measured using electrical probes. The ball-pen probe can be used to determine this quantity by fitting its current–voltage characteristics. The method is relatively simple, but requires a source of sweeping voltage. The ion temperature is obtained from the exponential part of the electron branch (${\displaystyle V_{probe}>\mathrm{\Phi }}$) of the current–voltage characteristic, as described below:

${\displaystyle I(V_{probe})=I_i^{sat}\left[R\left(1+K(V_{probe}-\mathrm{\Phi })\right)-\exp \left(\frac{\mathrm{\Phi }-V_{probe}}{T_i}\right)\right]}$

where ${\displaystyle I_i^{sat}}$ denotes the ion saturation current (${\displaystyle A_i{j}_i^{sat}}$), and the coefficient ${\displaystyle K}$ represents a generally observed linear increase with ${\displaystyle K>0}$ electron current (${\displaystyle K=0}$ for fully saturated case), combined with an exponential dependence describing the ion current, which is governed by the ion temperature ${\displaystyle T_i}$.

The main advantages of this method include:

• Robust and local measurements, making it suitable for both small and large fusion devices (COMPASS, Wendelstein 7-X)
• A relatively high level of the effective probe signal (${\displaystyle I_i^{sat}}$), which enables the use of a fast voltage sweeping regime and allows high temporal resolution (on the order of ${\displaystyle 5\text{–}10\mu \text{s}}$).