^{1,a)}, D. Dandurand

^{1}, T. Gray

^{1}, M. R. Brown

^{1}and V. S. Lukin

^{2}

### Abstract

A simple cylindrical Mach probe is described along with an independent calibration procedure in a magnetized plasmawind tunnel. A particle orbit calculation corroborates our model. The probe operates in the weakly magnetized regime in which probe dimension and ion orbit are of the same scale. Analytical and simulation models are favorably compared with experimental calibration.

This work was supported by grants from the Department of Energy, the National Science Foundation (CMSO), and the Office of Naval Research. The authors gratefully acknowledge the assistance of S. Palmer, J. Haldeman, A. H. Glasser, M. Korein, B. Gerber-Siff, K. Labe, and D. Weinhold.

I. INTRODUCTION

II. THEORETICAL MOTIVATION

III. SSX MACH PROBE AND WIND TUNNEL

A. Data

B. Analysis

IV. PARTICLE SIMULATIONS

V. DISCUSSION AND SUMMARY

### Key Topics

- Mach numbers
- 39.0
- Calibration
- 18.0
- Wind tunnels
- 17.0
- Plasma flows
- 12.0
- Magnetic fields
- 10.0

## Figures

Mach probe and magnetic probe setup inside the SSX plasma wind tunnel. The dimensions of the tunnel are . Device coordinates are as indicated with the θ-direction pointing into the page and the *z* along the magnetic probe. The *r*-direction is radially out from the axis. The plasma originates from the electrode and flows in the positive *z*-direction (from right to left in the figure).

Mach probe and magnetic probe setup inside the SSX plasma wind tunnel. The dimensions of the tunnel are . Device coordinates are as indicated with the θ-direction pointing into the page and the *z* along the magnetic probe. The *r*-direction is radially out from the axis. The plasma originates from the electrode and flows in the positive *z*-direction (from right to left in the figure).

Close-up of Mach probe showing orientation of the electrode collector areas and device coordinates. Probes are numbered clock-wise beginning bottom-right (e.g., probes 3 and 6 form the θ pair).

Close-up of Mach probe showing orientation of the electrode collector areas and device coordinates. Probes are numbered clock-wise beginning bottom-right (e.g., probes 3 and 6 form the θ pair).

Typical current measurements for each of the six electrode collectors of the Mach probe with channels labeled. The currents from each probe face have been offset by 0.7 A for clarity.

Typical current measurements for each of the six electrode collectors of the Mach probe with channels labeled. The currents from each probe face have been offset by 0.7 A for clarity.

*T* _{ e } was determined using VUV spectroscopy and *T* _{ i } with the IDS. Note that *T* _{ e } remained below 15 eV for the duration of the discharge and that *T* _{ i } > *T* _{ e } early in time.

*T* _{ e } was determined using VUV spectroscopy and *T* _{ i } with the IDS. Note that *T* _{ e } remained below 15 eV for the duration of the discharge and that *T* _{ i } > *T* _{ e } early in time.

Using Eq. (3), the sound speed is calculated as a function of time.

Using Eq. (3), the sound speed is calculated as a function of time.

|**B**| as a function of time for a single discharge. Measurements are displayed for probes 5, 8, and 12 of the linear array, 24.2, 38.6, and 58.0 cm from the first magnetic probe, respectively, beginning with the top trace. Squares indicate the time of detection the leading edge as the plasma approaches each probe. The magnetic field strengths have been offset for clarity.

|**B**| as a function of time for a single discharge. Measurements are displayed for probes 5, 8, and 12 of the linear array, 24.2, 38.6, and 58.0 cm from the first magnetic probe, respectively, beginning with the top trace. Squares indicate the time of detection the leading edge as the plasma approaches each probe. The magnetic field strengths have been offset for clarity.

The initial plume velocity, , determined using a linear array of magnetic probes. Using the slope of a linear regression of the mean arrival times (squares) for each probe, *v* _{ d } = 55.1 ± 6.4 km/s for data aggregated over 40 discharges.

The initial plume velocity, , determined using a linear array of magnetic probes. Using the slope of a linear regression of the mean arrival times (squares) for each probe, *v* _{ d } = 55.1 ± 6.4 km/s for data aggregated over 40 discharges.

Mach number in the (a) *z*-direction and (b) θ-direction for LH and RH shots aggregated over 20 discharges in each orientation. Peak initial *M* _{ z } flows are observed at approximately 32 μs. Note that very little azimuthal flow is observed in the initial plume.

Mach number in the (a) *z*-direction and (b) θ-direction for LH and RH shots aggregated over 20 discharges in each orientation. Peak initial *M* _{ z } flows are observed at approximately 32 μs. Note that very little azimuthal flow is observed in the initial plume.

Absolute flow velocities in the (a) *z*-direction and (b) θ-direction. Data included for LH and RH shots aggregated over 20 discharges.

Absolute flow velocities in the (a) *z*-direction and (b) θ-direction. Data included for LH and RH shots aggregated over 20 discharges.

Simulation plot of z-directed Mach number (using the expression (*M* _{1} + *M* _{2})/2cos 30°) versus the exact input Mach number (defined by *v* _{ d }/*v* _{ th }). The error bars are smaller than the resolution of the graph. A linear least-squares fit to the data gives an implied calibration constant of *K* = 2.61 ± 0.01.

Simulation plot of z-directed Mach number (using the expression (*M* _{1} + *M* _{2})/2cos 30°) versus the exact input Mach number (defined by *v* _{ d }/*v* _{ th }). The error bars are smaller than the resolution of the graph. A linear least-squares fit to the data gives an implied calibration constant of *K* = 2.61 ± 0.01.

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