# deHoffmann-Teller Analysis

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### Contents:

- Overview
- Inputs
- Outputs
- Bugs/Caveats
- History
- Other MPE/ISSI PlugIns

### Overview

DeHoffmann Teller (HT) analysis basically consists of calculating a frame of reference in which the electric field vanishes. The velocity of this frame can under certain conditions be regarded as the motion speed of a rigid plasma structure, e.g., a plasma bubble or a plasma boundary like e.g., the magnetopause.

An optional plasma density may be supplied. The Alfven velocity is then calculated. The velocity relative to the deHoffmann-Teller velocity may then be compared with the Alfven speed. A component-by-component plot of these two quantities - a Walen plot - may give an indication of reconnection. If the two quantities are nearly proportional, it may be an indication of reconnection.

The calculated Alfven velocity is corrected for effects of pressure anisotropy if the perpendicular and parallel temperatures are supplied in slots 4 and 5. If the temperature is available as a tensor (e.g., THEMIS plasma data), this tensor should be dropped in slot 4 -' Optional pParallell temp'. Leave slot 5 empty (or enter '0') in this case.

DeHoffmann-Teller analysis is described in Chapter 9 of the book 'Analysis Methods for Multi-Spacecraft Data', ISSI, 1998 or Chapter 7 of 'Multi-Spacecraft Methods Revisited, ISSI, 2008 (both books available from www.issi.unibe.ch:issi_sr.html).

### Input data

Required inputs are a magnetic field vector time series and either plasma velocity time series or an electric field time series (the Plugin will consult the metatag 'units' to determine whether a velocity or electric field was given). If a velocity is given, the electric field is calculated as E = -V x B.

Optional inputs :
An optional plasma density may be supplied to calculate the Alfven velocity.
If the density is supplied, optional temperatures may be supplied. The Alfven velocity will then be corrected for pressure anisotropies. The temperatures can be supplied as two separate time series containing the perpendicular and parallel temperature, or alternatively, as a temperature tensor. In the latter case, drop this tensor in slot 4 - 'Optional pParallell temp', and leave input slot 5 empty (or enter '0').

Also, an optional normal unit normal, e.g., a boundary normal may also be supplied - the HT velocity along this normal is then calculated. The nomal may be a QSAS object or can be typed directly in the input slot as text on the form '[x, y, z]'. Ignore the red background in the latter case.

### Outputs

Output quantities are:
- E_HT - vector time series with the Hoffmann-Teller electric field
- E_C - vector time series with the convective electric field (E= V x B)
- V_VHT - vector time series with the rest velocity, i.e. (V(i) - V_HT)
- V_Alfven - vector time series with the Alfven velocity. Only valid if density is supplied

In addition, the each time interval, number of samples, the complete HT velocity, and accelleration is printed in the PlugIn output window. If a boundary normal is supplied in the Normal slot, the velocity and acceleration along this normal is also printed

For ISSI/MPE only : The rest velocity and the convective velocity is written to the file /tmp/qsas_dht.txt. This file can be used by various utility programs to generate the above described Walen plot.

### Bugs/Caveats

None known.

### History

2009-01-05 : updated documentation

2008-01-30 : fix Themis SI temperature conversion

2008-01-21 : fix to allow THEMIS temperature tensor

2005-05-13 : catch singularity in 1-alpha correction

2005-01-30 : corrected bug in pressure correction (Pperp and Ppar were swapped)

SEH, 5 Jan 2009