plasma adiabaticity in a diverging magnetic …peplweb/pdf/icops2014_sheehan2.pdf · plasma...

PLASMA ADIABATICITY IN

A DIVERGING MAGNETIC NOZZLE

J. P. Sheehan and Benjamin W. Longmier University of Michigan

Edgar A. Bering University of Houston

Christopher S. Olsen, Jared P. Squire, Mark D. Carter,

Franklin R. Chang Díaz, Timothy W. Glover,

Andrew V. Ilin, and Leonard D. Cassady Ad Astra Rocket Company

ABSTRACT

We propose a fluid model for ambipolar ion acceleration in a magnetic

nozzle that preserves the adiabaticity of the plasma. This adiabatic theory

predicts that the change in average electron energy depends linearly on

the change in plasma potential, providing an important design metric for

electric propulsion devices which employ magnetic nozzles. The fluid

theory predictions were compared to measurements made in the VASIMR

VX-200 experiment which has conditions conducive to ambipolar ion

acceleration. A planar Langmuir probe was used to measure the plasma

potential, electron density, and electron temperature for a range of mass

flow rates (50 – 140 mg / s) and power levels (12 – 30 kW). The linear

relationship between electron temperature and plasma potential was

observed as predicted. The adiabatic theory relies on collisions to

rethermalize the electrons and establish a temperature gradient. Coulomb

collisions cannot account for the high collisionality but an ion acoustic

instability may enhance the collision frequency.

2 41st IEE International Conference on Plasma Science

Washington DC, May 28, 2014

HELICONS AND MAGNETIC NOZZLES FOR

APPLICATIONS IN PROCESSING AND PROPULSION

Helicons

Radio frequency

High ionizing efficiency

Electron heating

Magnetic nozzle

Functions like physical

nozzle

Accelerates ions

Converts thermal energy

into directed kinetic

energy

Applications

Materials processing

Electric propulsion

CHI KUNG

VASIMR



CURRENT FREE DOUBLE LAYERS

IN HELICON EXPERIMENTS

Narrow layer (10s of λd) of large

potential jump (several Te/e)

Isothermal

Occurs downstream of nozzle

Current free, expanding

Accelerates ions

May be thrust mechanism in helicon

thrusters

Open question of how/why current

free double layers form



ION ACCELERATION IN VASIMR

VASIMR: < 200 kW helicon + ICH

thruster

Went looking for double layers, but

found none!

Vp, ne, and Te derivatives coincide

Long length scales: 10,000s of λd

λd ~ 10 μm

Corroborated with RPA

B. W. Longmier et al., Plasma

Sources Sci. Technol. 20, 015007

(2011).



PLASMA IN NOZZLE IS ADIABATIC

Assume plasma is adiabatic

Energy loss to surfaces small

Radiation loss small

Geometry dictates degrees of freedom (N)

Expanding plasma sphere: N = 3

Magnetic nozzle: N = 2

Electrons remain Maxwellian, though

temperature can change

Relies on collisions

Conservation of momentum

Relationship between average electron energy

loss and potential (→ion energy gain)



HELICON EXPERIMENT

USING VASIMR HARDWARE



• Bmax = 20,000 G

• P = 15 – 30 kW

• ṁ = 50 – 140 mg/s

• Only helicon coupler used, no ICH

• Superconducting magnets generate converging/diverging

magnetic field

MEASUREMENTS IN PLUME WERE MADE

WITH PLANAR LANGMUIR PROBE

Vp < 20 V

Te < 15 eV

ne = 1010 – 1012 cm-3

Planar tungsten probe

No RF compensation

needed

Guard ring reduces

sheath expansion

effects

Parameters extracted

from I-V traces

Vp: knee

Te: semilog fit

ne: saturation

current



PARAMETRIC STUDY

OF OPERATING PARAMETERS

Measured at fixed position

50 cm from throat

Highest density where probe

could survive

Lower mass flow rate

Higher Te, Vp

Lower ne

Power flow density ∝ input

energy per ion

Optimize energy deposition

for given flow rate



Vp, Te, ne DECAY DOWNSTREAM

Axial measurements

Lowest and highest mass flow

rates are shown

Low flow rates → high

temperature, larger

gradients

Temperature decay: plasma is

not isothermal

Length scale: 10,000s of λd

No double layer, but

significant density and

temperature gradients



DATA WERE CONSISTENT

WITH ADIABATIC THEORY

Plasma potential decays

proportionally to electron

temperature

Only parallel electron temperature

was measured with planar probe

Some electron energy may be lost

to other sinks

Collisions

Instabilities

Radiation

J. P. Sheehan et al., Plasma Sources

Sci. Technol., (submitted).



ALTERNATIVE THEORY:

RAREFACTION WAVE THEORY

Nonlocal theory

Far downstream,

rarefaction waves create

potential structures which

confine electrons

Electrons lose energy on

wave, cooling in

downstream region

Two regions

Steady state: ambipolar

ion acceleration

Rarefaction wave: further

acceleration

Steady-state part

Rarefaction wave part

Arefiev and Breizman, Phys. Plasmas 16, 055707 (2009).



COMPARISON BETWEEN ADIABATIC THEORY

AND RAREFACTION WAVE THEORY

Fundamental difference: local

theory or non-local theory

Both predict same relationship

between φ and Te

Different relationship between φ

and ne

Suggests some discrepancy in

number of degrees of freedom

No observed acceleration in low-

field region

Factor of 3 increase in ion

velocity from rarefaction

wave

Importance of collisions

Rarefaction wave theory

Experiment



ADIABATIC THEORY RELIES ON

COLLISIONS, RETHERMALIZATION

VASIMR has >95% ionization

fraction → Coulomb collisions

dominate

Electron-electron collisions cause

rethermalization of EVDF

Collisions necessary to reduce

thermal conductivity along field

lines

Classical coulomb collision are

insufficient to explain

rethermalization

Collisional mean free path only

becomes long enough after major

temperature gradient



PLASMA IS DETACHED FROM

MAGNETIC FIELD LINES

In a fully attached nozzle, density

should follow field lines

ne/B > 1

Plasma beam more focused

Detachment occurs

Possible detachment mechanisms

Particle collisions

Anomalous transport

Demagnetization

Frozen flow

Electron inertia

C. S. Olsen et al., IEEE Trans. Plasma

Sci. (accepted, 2014).



INSTABILITIES INCREASE

THE COLLISION FREQUENCY

In the kinetic equation, collisions represented by collision operator

which has depends on the collisional kernel

Collision frequency affected by both the stable and unstable parts

S. D. Baalrud, J. D. Callen and C. C. Hegna, Phys. Rev. Lett. 102, 245005 (2009).



AMBIPOLAR ION ACCELERATION SCALES

ARE SIMILAR TO PRESHEATH SCALES

LE, LB, λcx >> λd

vi ~ cs

Presheath and sheath

Ti << Te

Δφ ~ Te

Quasineutral

J = 0

Ambipolar acceleration



CONVECTIVE ION ACOUSTIC INSTABILITY

INCREASES DOWNSTREAM COLLISION FREQUENCY

Electron-electron collision frequency

in magnetic nozzle without

considering parameter gradients

In presheath:

Te constant

ne ~ constant

In magnetic nozzle:

dTe/dx ~ Te/LB

dne/dx ~ ne/LB

Instability grows as ions propagate

Collisions rethermalize electrons

Ignoring gradients (see figure)

overestimates collision frequency

Complicating factors

Ion temperature, i-n collisions

Magnetic field divergence



CONCLUSIONS

Ambipolar ion acceleration

observed in VX-200 experiment

Longer length scale than in

CFDLs

Adiabatic theory describes

experimental results

Potential drop depends on

temperature, not density

Local vs. non-local theory—

unresolved questions

Unknown cause of

rethermalization

Proposed collision mechanism:

ion acoustic instability





LEAVE NAME AND EMAIL

FOR A COPY OF THE POSTER

plasma adiabaticity in a diverging magnetic …peplweb/pdf/icops2014_sheehan2.pdf · plasma...

Documents