CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUELaboratoire de Physique et Chimie de l'Environnement et de l’Espace

3A, avenue de la Recherche ScientifiqueF-45071 Orléans cedex 02, France

Phone: (33 2) 38 25 52 63; Fax: (33 2) 38 63 12 34; E-mail: Jean-Gabriel.Trotignon@cnrs-orleans.fr

EJSM JGO/RPWI Team Meeting, Warsaw, 10-11 Jan. 2011

Mutual Impedance MEasurements, MIME as part of the EJSM JGO/RPWI

Jean Gabriel TROTIGNON and the MIME Team

LPC2E, CNRS, Université d’Orléans, Orléans, France

EJSM JGO/RPWI Team Meeting, 10-11 Jan. 2011

Mutual Impedance MEasurements, MIME as part of the EJSM JGO/RPWI

Téléphone: (33 2) 38 25 52 63 Secrétariat: (33 2) 38 25 52 64 Télécopie (Fax): (33 2) 38 63 12 34 E-mail: Jean-Gabriel.Trotignon@cnrs-orleans.fr

MIME general status

Mutual-Impedance considerations

Conclusion

Olivier Le Duff presentation

Presentation Outline

MIME general status

MIME actions:  To fill in DPU, RPWI DCDC, Mechanical, and Miscellaneous Questionnaires (Done).

To estimate instantaneous data rate, compression factor, compressed data rate to S/C OBDH, and total data volume to be downlinked (Done).  To sign “Non-disclosure agreement and declaration of non-interest for participants in the EJSM/Laplace DOI instrument study teams” (Done).

Application for funding (submitted to CNES, and funding secured for 2010 and 2011).

To provide the list of people in charge of MIME (to be updated) Science: Jean Gabriel Trotignon Jean Louis Rauch + Aurélie Marchaudon and Jean Pierre Lebreton Technology: Olivier Le Duff (TM) + Fabrice Colin

MIME general status (cont’d)

MIME actions (cont’d): 

RPWI-13: Include Active Measurements Capability (Done)

“Mutual Impedance Measurements, MIME”, by J. G. Trotignon , J. L. Rauch, and F. Colin

1 Introduction 2 How do standard impedance probes work? 2.1 Self-impedance measurements 2.2 Mutual-impedance measurements 3 Advantages of quadripole probes 4 The MIP mutual impedance probe onboard ROSETTA 5 The MIME Mutual Impedance MEasurements 5.1 MIME scientific objectives 5.2 MIME principle of measurements 5.3 Expected MIME range of measurements 5.4 MIME measurement point definition 5.5 MIME possible working modes 5.6 MIME telemetry resources 5.7 Electric-field antenna/LP occupancy 5.8 MIME power and mass resources 5.9 How to implement active plasma measurements onboard EJSM/JGO 6 Conclusion

Mutual-Impedance considerations

A classical impedance probe consists in the probe itself and the electronics that measure the impedance:  The probe comprises transmitting/receiving electrodes immersed in the plasma.  The electronics measure the dynamic impedance between the electrodes at several fixed frequencies over a range that includes the electron plasma frequency, from which the total plasma density is directly derived. As the impedance depends on the parameters of the ambient plasma, such as the electron density and temperature, impedance probes are powerful tools for plasma diagnostics.

Mutual-Impedance considerations (cont’d)

Let us consider an infinite homogeneous plasma in which there is an alternating point source Q = Qo exp jωt , where ω is the angular frequency. The source emits a current I that produces an electric field E(r) .

In the quasi-electrostatic approximation (which is valid provided that the distance r is small compared with the wavelength of any electromagnetic wave that can be propagated in the plasma at the given frequency) E = - gradV.

The point-source transfer impedance function of the plasma is defined as:

Z(ω,r) = V(ω,r) / I = V(ω,r) / jωQ, indeed I = dQ/dt = jwQ.

(In vacuum Vo(ω,r) = Q / (4π εo r), therefore Zo(ω,r) = 1 / (4π jω εo r).

Let us now assume a cold plasma in the absence of a magnetic field, its dielectric constant is given by :

εr = 1 – (ωpe2/ω2) / (1 – j ν / ω),

where ωpe is the angular plasma frequency and v the collision frequency of electrons with heavy particles.

Mutual-Impedance considerations (cont’d)

In a uniform isotropic dielectric, the potential distribution set up by a point charge is:

V(ω,r) = Q / (4π εo εr r) = Vo / εr ,

and then Z = Zo / εr = Zo / [1 – (ωpe2/ω2) / (1 – j ν / ω)].

Source decourant

récepteur

E1

E2

R1

R2

plasmaSource decourant

récepteur

E1

E2

R1

R2

plasma

For a square aray quadripole probe, we obtain:

Z (ω) / Zo (ω,d) = 0,414 / [1 – (ωpe2/ω2) / (1 – j ν / ω)],

with Zo (ω, d) = 1 / (4π jω εo d),

where d is half the diagonal length.

And whenever the collision frequency ν is negligible,

Z (ω) / Zo (ω,d) = 0,414 / [1 – (ωpe2/ω2)] .

Mutual-Impedance considerations (cont’d)

If there are no collisions (dotted curve), Z (ω) / Zo (ω,d) = 0,414 / [1 – (ωpe2/ω2)],

the transfer impedance tends to infinity as the frequency approaches the plasma frequency (i.e. there is a resonance).

In the presence of collisions (solid curve), there is a simple maximum at a frequency slightly higher than the plasma frequency. The height of the maximum and the width of the peak depend on the ratio v/ωpe.

v/ωpe = 0

v/ωpe = 0.1

ω /ωpe

Mutual-Impedance considerations (cont’d)

Considering a cold plasma in the presence of B, but in the absence of collisions.It is anisotropic, and εr is now a tensor:

| S j D 0 |εr = | - j D S 0 | ,

| 0 0 P |

Its diagonal elements are: S = 1 - Σi ωpi2 / (ω2 - ωci

2)

and P = 1 - Σi ωpi2 / ω2 ~ 1 - ωpe

2 / ω2 ~ εro (B = 0, and no collisions).

Note: P is the dielectric constant in the absence of B; P = S and D = 0 in the absence of B, the tensor is then diagonal.

After some computations that are out of the scope of this presentation, the point-source transfer impedance function Z(ω,r) for a cold and magnetized collisionless plasma:

• Becomes infinite at the upper and lower hybrid frequencies, and under conditions corresponding to the oblique resonance;• May be very large at the composite plasma frequency; and• Vanishes at the electron and ion gyrofrequencies.

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUELaboratoire de Physique et Chimie de l'Environnement et de l’Espace

3A, avenue de la Recherche ScientifiqueF-45071 Orléans cedex 02, France

Phone: (33 2) 38 25 52 63; Fax: (33 2) 38 63 12 34; E-mail: Jean-Gabriel.Trotignon@cnrs-orleans.fr

Mutual Impedance MEasurements, MIME as part of the EJSM JGO/RPWI

J. G. Trotignon and the MIME Team

Conclusion

Mutual Impedance probes, and in particular quadripole probes (in asymmetrical and/or symmetrical configurations) can be used for measuring characteristic frequencies of a magnetoplasma, thus allowing powerful plasma diagnoses to be done.

MIME may therefore contribute to the study of the Jupiter’ system and also help out with in-flight sensor calibrations.

EJSM JGO/RPWI Team Meeting, Warsaw, 10-11 Jan. 2011