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title: Mach probe ring
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This page was last updated on 14 March 2019.

#Introduction

A ring of 8 Mach probes is available at tokamak GOLEM, offering measurements of the toroidal Mach number $M = v_{t}/c_{s}$, where $v_t$ is the plasma toroidal rotation velocity and $c_s$ is the ion sound speed.

Note: As of November 2018, one of the probes is missing a part (see section Probe connection scheme), so effectively only 7 Mach probes are fully available. The ring is not currently installed in the tokamak, but it is available upon request from Vojtech Svoboda.

[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_ring_front.JPG" width="225" height="300" />](/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_ring_front.JPG)
[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_ring_back.JPG" width="225" height="300" />](/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_ring_back.JPG)
[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_ring_closeup.JPG" width="300" height="225" />](/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_ring_closeup.JPG)
[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/single_mach_probe.JPG" width="300" height="225" />](/Diagnostics/ParticleFlux/MachProbeRing/single_mach_probe.JPG)
[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/connector.jpg" width="300" height="225" />](/Diagnostics/ParticleFlux/MachProbeRing/connector.jpg)
[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/cimg8654.jpg" width="300"/>](http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/cimg8654.jpg)
[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/cimg8655.jpg" width="300"/>](http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/cimg8655.jpg)

#Measurements provided by the Mach probe

In general, a Mach probe consists of two flat Langmuir probes, both biased to a negative potential $\sim -100$ V, which are placed close together but electrically insulated from one another. Assuming then that both the probes have the same effective collection area, the Mach number can be calculated from their respective ion saturation currents $I_{sat}$ using the formula

$M = \frac{I_{sat1} - I_{sat2}}{I_{sat1}+I_{sat2}}.$

For more information, see [this document](https://dspace.mit.edu/bitstream/handle/1721.1/54615/600142320-MIT.pdf) detailing Mach probe measurements at the Versatile Toroidal Facility at MIT, Massachusetts.


#Probe geometry


[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_size.jpg" width="225" height="300" />](/Diagnostics/ParticleFlux/MachProbeRing/mach_probe_size.jpg)

The electrode dimensions are 4 mm by 8 mm. Other dimensions are drawn in the picture above.

#Probe connection scheme

[<img src="http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/MachProbeRing/mach_probe.svg" width="600" height="649" />](/Diagnostics/ParticleFlux/MachProbeRing/mach_probe.svg)

The probes are mounted on a ring which originally carried 128 Langmuir probe pins. The pins have been removed, as the fourth photo above shots, and in their place the Mach probes have been installed. This means a great redundancy of wires - there are 128 wires and 128 output connectors, but only 16 are in use. This section presents the probe connection as measured in November 2018. The naming scheme described in the picture above is used:

- when viewed from the front (the first photo), the Mach probes are labeled 1-8, with front (f) and back (b) electrodes
- the wires are then connected into one of the four inner connector arrays (A and B from the front, C and D from the back, with 32 pins each)
- finally the data can be collected from the output connectors (labelled 1-4, with 32 pins each)

Using these labels, the following table sums up the probe connections.

| electrode | inner connector | output connector | <span style="color:white">sblank space</span> | electrode | inner connector | output connector |
|:---:|:-------:|:------------:|:---:|:---:|:-------:|:------------:|
| 1f | 1D | 4-31 | | 1b | 1B | 4-30 |
| 2f | 9B | 4-14 | | 2b | 9D | 4-15 |
| 3f | 18D | 3-29 | | 3b | 16B | 3-31 |
| 4f | 25D | 3-12 | | 4b | electrode missing | electrode missing |
| 5f | 31C and 32C | 2-27 | | 5b | 31A and 32A | 2-28 |
| 6f | 22C | 2-15 | | 6b | 22A | 2-12 |
| 7f | 16A | 1-31 | | 7b | 14C | 1-30 |
| 8f | 8A | 1-15 | | 8b | 6C | 1-14 |