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# Rake probe

This page was last updated on 5 March 2019.

# Introduction

The rake probe consists of a row of 16 cylinder Langmuir probes, each connected to an output connector. It is, therefore, ideal for profile measurements. Usually, Langmuir probes are used in one of the three regimes:

- floating potential \(V_{fl}\) (probe electrically isolated)
- ion saturated current \(I_{sat}\) (probe biased to a stable, negative potential \(\sim -100\) V)
- probe \(I-V\) characteristic (bias potential sweeping) - electron temperature \(T_e\), plasma potential \(\Phi\), floating potential \(V_{fl}\), ion saturated current \(I_{sat}\), electron energy distribution function…

Combining these measurements on shot-to-shot basis, one may also obtain the electron density \[n_e = \frac{I_{sat}}{feA\sqrt{2eT_e/m_i}}\] where \(f=\frac{1}{2}\) is a factor related to the plasma density fall inside a sheath, \(e=1.60 \times 10^{-19}\) C is the elementary charge, \(A \approx 8.8 \times 10^{-6}\) m\(^2\) is the effective probe collecting area (approximated by the total probe surface area) and \(m_i\) is the ion mass (\(m_i = 1.67 \times 10^{-27}\) kg for hydrogen), and the parallel heat flux \[q_\parallel = \gamma \frac{I_{sat}T_e}{A}\] where \(\gamma \approx 7\) is the sheath heat transmission coefficient.

It is widely recognized that Langmuir probes are important tools for studying edge plasma physics in tokamaks because of the required space resolution (in the range of several ion Larmor radii) and a high temporal resolution (of about 1 \(\mu\)s or even better) can be easily achieved. Therefore, they are routinely used on any tokamak facility.

# Rake probe geometry

- total number of pins: 16 (all connected)
- pin width: 0.7 mm
- pin length: 4 \(\pm\) 0.3 mm
- distance between pins: 2.5 mm
- sampling frequency: 1 MHz

At the moment, the probe is not installed in the tokamak. If it should be installed, please perform your own measurements of the manipulator length and the calculation of pin 1 position. You may refer to the old index page, but be critical.

# Theory of Langmuir probe measurements

(Excerpt from ZAVERYAEV et al.: Single Langmuir Probes. In http://www-pub.iaea.org/books/IAEABooks/8879/Fusion-Physics, M.Kikuchi, K.Lackner, M. Quang Tran (Ed), IAEA, 2012, pp. 369-371. Reprinted with kind permission to reproduce IAEA materials.)

The theory of probes in general discussed in Refs [4.74–4.76]. In accordance with this theory, the usual method to determinate the values of electron temperature and density with a probe is to register the current–voltage characteristics. Figure 4.3 shows typical current–voltage characteristics of different kinds of electrical probes in a plasma consisting of electron and singly charged ions, where both particle species have a Maxwellian energy distribution. A conventional analysis of such characteristics involves fitting the data up to the voltage at which electron current saturates with the standard Langmuir formula:

\(I(V)=I_{i,sat}(1-\mathrm{e}^{(V-V_{fl})/T_e})\)

where \(I\) is the current drawn by the probe at applied voltage \(V\), \(I_{i,sat}\) is the ion saturation current, \(T_e\) is the electron temperature and \(V_{fl}\) is the floating potential of the probe.