Spinning an Unmagnetized Plasma for Magnetorotational and ...kunz/Site/PCTS_files/Modeling rot… · 23 Helium V o=6.5 km/s, n=2x1018 m-3, T e=8 eV, T i=1.5 eV, F. Ebrahimi, 2011

Spinning an Unmagnetized Plasma for Magnetorotational and

Dynamo Experiments

Cary Forest , Mike Clark, John Wallace, Carl Wahl, Blair Seidlitz, Chris Cooper,

David Weisberg, Jason Milhone, Ken Flanagan, Ivan Khalzov, Fatima Ebrahimi

Princeton, NJ April 9, 2013

Cami Collins

University of Wisconsin - MadisonStability, Energetics, and Turbulent Transport

in Astrophysical, Fusion, and Solar Plasmas

Thursday, April 11, 2013

A New Frontier in Laboratory Astrophysics

2

Where do magnetic fields come from?

Why does matter rapidly fall inward in accretion disks?

dynamo? magnetorotational instability?

ρV2>>B2/µoRm=µoσVL>>1


Why Plasma? (instead of liquid metal)

-Explore large Rm and destabilize at lower B

-Vary Pm = µoσν from the liquid metal/protoplanetary disk regime (Pm<<1) to black hole, neutron star disk (Pm>>1)

-Study effects beyond ideal MHD (two fluid Hall effect, plasma-neutral interactions, compressiblity)

3


4

Plasma Couette Experiment Madison Plasma Dynamo Experiment

•Challenge: -Need confinement for plasma to be hot (σ) and dense (ρ) -Difficult to drive flow in an unmagnetized plasma

Laboratory Studies of Flow-Driven MHD Instabilities


•Confining and stirring an unmagnetized plasma in the Plasma Couette Experiment (PCX)

•Creating flow profiles to study the magnetorotational instability, a mechanism thought to be important in accretion disks

•Application of this new stirring technique for dynamo studies in MPDX

Outline

5


(Keplerian)

•Keplerian flows of conducting fluids are hydrodynamically stable

•Can be destabilized by a magnetic field: the magnetorotational instability (MRI)

(Couette)

Couette Flow of Plasma

6

!"

!

!

Bz


+-

B

E

V

S N S N

S

The Concept: Create Plasma Rotation Using Biased Cathodes

7

Anodes

PCX Magnetic Geometry

0.6

0.4

0.2

0

0 0.1 0.2 0.3 0.4 0.5R [m]

Z [m

]

Hot Cathodes

Initial Setup for Spinning from Outer Boundary

•Toroidally localized electrodes are biased to create JxB torque

•Velocity couples inward through viscosity

•Rotation is axisymmetric

Cathode

Mach Probeunmagnetized


8

He Velocity Profile2 Outer Cathodes Biased 550 V

(measured with Mach probe) ECH

CurrentPressure

Density

TeRotation Driven

At Magnetized Edge

Vϕ couples inwardthrough viscosity

The Rotation Scheme Works!

Pm~10 Rm~50Thursday, April 11, 2013

9

ECH

CurrentPressure

Density

Te

The Rotation Scheme Works!

He Velocity Profile2 Outer Cathodes Biased 550 V

(measured with Mach probe)


10

Ion Centrifugal Force is Balanced by Electron Pressure

Electron force balance:

Ion force balance:


11

Radial Electric Field Measurement in Spinning Plasma

2 cm

Mach Probe

Tips to MeasureFloating Potential

Ar Floating Potential Profile

Location of Anode


12

Electric Field and Velocity Measurements Agree

5.5 V/m 2 km/s

Ar Floating Potential Profile Ar Velocity Profile


13

Viscosity Competes with Neutral Drag as Velocity Spreads Inward

edge-applied torque drag term, from ion neutral cx

viscosity couples momentum inward

Steady state velocity profiles can be calculated using measured plasma parameters (n, Te, neutral pressure) and modified Bessel functions:

where the characteristic momentum diffusion length scale is:

(without neutral drag, the solution is Couette flow)


Viscosity Can Be Estimated By Fitting Velocity Profiles

14

Viscosity [m

2/s]

Future plans to measure Ti and confirm Braginskii viscosity

Ar Vϕ


15

Viscosity [m

2/s]

Braginskii Viscosity Depends on Magnetization

Ar Vϕ

Ar νBraginskii, Sec. 4, (1965)


16

Viscosity [m

2/s]

Helium is less viscous in the

magnetized region

Helium has much smaller

ionization fraction

Ar Vϕ

Ar ν

He Vϕ

He ν

Neutral Drag Modifies Profiles

[PRL 108, 115001 (2012)]


17

Next Step: Rotate from the Inner Boundary

KeplerianSolid Body

Couette


18

Pulley for raising and lowering center stack

into garage

Cathodes are heated tungsten filaments

Center Stack

Center Stack Assembly for Inner Boundary Rotation


19

AnodesHot Cathodes

νum /10 [m2/s]

νm /10 [m2/s]

Bz [mT]

Cathode Placement is Critical

ωci τii


20

Helium, 3 Inner Cathodes500 V inner, 400 V outer

Outer Cathodes (A)

Inner Cathodes (A)

ECH (kW)Pressure (Torr)

Te (eV)

n (m-3)

Spinning from the Inner Boundary


21

500 V inner, 400 V outer


Spinning from the Inner Boundary

Ti 0.11 eV 0.216 eV 0.25 eV 0.32 eVTe 5.9 eV 5.3 eV 6.5 eV 7.5 eV

n x1016 cm-3 1.7 1.8 2.4 2.3Ionization 0.35% 0.37% 0.74% 0.65%

Pm 0.2 0.88 1.3 2.9Rm 19 25 46 64

Rm_inner 5.1 10 11 17



3 Inner Cathodes 5 Inner Cathodes


22

•To observe MRI, we simply need a weak seed field and Keplerian-like rotation that satisfies:

BRIEF ARTICLE

THE AUTHOR

(γ + Pm)(γ + 1) + S2

2(1 + 2) + 2ζR2

m(γ + 1)2 − 2(2− ζ)R2

mS2

+ηH

η

(γ + Pm)

2+

2ζR2m

(1 + 2)

(ζ − 2)Rm +

ηH

η

+ S2Rm(ζ + 2)

= 0

Pm =νη S =

kzVAηk2 Rm =

Ωηk2 γ =

γηk2 ηH =

Boµone

ζ =1

rΩ∂(r2Ω)

∂r =

h

(r2−r1)

kz =πh

kr =π

(r2−r1)

if vi = v, and j = e(nivi − neve), then ve = v − jne

Ohm’s law becomes E + v ×B = ηj +1ne

j×B

v =− ∂Φ

∂rBo

∂Ω∂r

< 0

∂(r2Ω)∂r

> 0

1

BRIEF ARTICLE

THE AUTHOR

(γ + Pm)(γ + 1) + S2

2(1 + 2) + 2ζR2

m(γ + 1)2 − 2(2− ζ)R2

mS2

+ηH

η

(γ + Pm)

2+

2ζR2m

(1 + 2)

(ζ − 2)Rm +

ηH

η

+ S2Rm(ζ + 2)

= 0

Pm =νη S =

kzVAηk2 Rm =

Ωηk2 γ =

γηk2 ηH =

Boµone

ζ =1

rΩ∂(r2Ω)

∂r =

h

(r2−r1)

kz =πh

kr =π

(r2−r1)

if vi = v, and j = e(nivi − neve), then ve = v − jne

Ohm’s law becomes E + v ×B = ηj +1ne

j×B

v =− ∂Φ

∂rBo

∂Ω∂r

< 0

∂(r2Ω)∂r

> 0

1

Profiles are Approaching MRI Unstable Regime

-Note: still need to turn on the Bz field (may change filament placement)


23

HeliumVo=6.5 km/s, n=2x1018 m-3, Te=8 eV, Ti=1.5 eV,

F. Ebrahimi, 2011

•MRI growth rates can be estimated by a local stability analysis of incompressible, dissipative MHD with Hall term.

•The Hall term becomes important when ions are decoupled from the B field (ex: collisions with neutrals or finite device size)

•Result: Large growth rate appears only when B is antiparallel to Ω

MRI Growth Rate (global NIMROD simulation vs. local WKB)

-15 -10 -5 0 5[Gauss]

Local

-15 -10 -5 0 5[Gauss]

Local Global

What Would the MRI Look Like?


24

Ion Neutral Drag term

Hall term

n=3x1010 cm-3

P=1x10-4 TorrTe=5.3 eVTi=.216 eV

How Does Ion-Neutral Drag Affect MRI?

Helium

Vinner=4.25 km/sVouter=5.5 km/s


25

Velocity and Magnetic Field Structures Appear in the Saturated State, Which Depend on the Hall Term

MHD

HALL

[km/s]

F. Ebrahimi, 2011


26

Hydrodynamic Stability of Viscous Couette Flow with Drag

Linearized momentum eq. + continuity eq. results in:

Chandrasekhar 1961Taylor 1923

Consider perturbations of the form:


27

When is Viscous Couette Flow with Drag Unstable?

Rayleigh line

Marginal stability analysis with neutral-damping

unstable

stable

-Taylor vortices could occur at high Vinner, low viscosity-What are the boundary conditions?

Taylor (1923)

Reouter=VoL/ν

Re i

nner

=V

iL/ν


28

Why Not Run Full Blast?

Before After

heating/arcing issues


29

Laser Induced Fluorescence In Progress

Laser Excitation1047.00475 nm


30

Laser Induced Fluorescence In Progress

Ti = 0.058 eV ± 4.4%

Laser Excitation1047.00475 nm


31

The Madison Plasma Dynamo Experiment

•3 m diameter sphere•strong magnets = good confinement•fully ionized (200 kW LaB6 + ECH)•Goal: Rm ~ 2000


32

Electrostatic Biasing Controls Edge Rotationpla

sm

aw

illrequir

e0.5

MW

.

S

N S N S N

+-

BE

V

Fig

ure

3:

Ele

ctrode

driv

efo

rflow

.A

lternat-

ing

posit

ive

and

negativ

eele

ctrostatic

bia

sis

applied

to

ele

ctrodes

betw

een

cusp

rin

gs.

The

result

ing

E×

Bvelo

city

ispurely

toroid

aland

controllable

.

Pla

sma

Rot

atio

nC

ontr

ol.

The

multid

ipole

geom

-

etry

allow

sa

sim

ple

and

robust

ele

ctrode

schem

e

to

driv

ethe

velo

city

field

inthis

geom

etry.

The

geom

etry

isshow

nin

Fig

.3.

The

concept

isto

use

toroid

ally

sym

metric

ele

ctrodes

betw

een

each

of

the

cusp

rin

gs,

and

to

apply

alternatin

gpos-

itiv

eand

negativ

epotentia

lsto

these

ele

ctrodes.

The

result

ing

ele

ctric

field

alt

ernates

inpola

rity,

whic

h,

together

with

the

alt

ernatin

gdir

ectio

nof

the

magnetic

field

giv

es

auniform

E×

Bvelo

c-

ity

inthe

toroid

aldir

ectio

n.

The

ele

ctrode

schem

e

mim

icsthe

boundary

conditio

nsthata

rotatin

gves-

sel

would

provid

ein

fluid

mechanic

sexperim

ents

(w

here

no

slip

condit

ions

can

be

assum

ed).

Sin

ce

the

UE×

Bvelo

city

can

be

estim

ated

on

the

surfa

ce

of

the

magnets

from

the

magnitude

of

the

potentia

ldrop,

the

dis

tance

betw

een

the

flux

surfa

ces,and

the

strength

ofthe

magnetic

field

on

the

surfa

ce

ofthe

magnets,it

can

be

proje

cted

into

field

lines

deeper

inthe

sphere.

We

pla

nto

insert

the

cathodes

into

magnetic

field

lines

whic

hare

separated

by

1cm

on

the

surfa

ce

ofthe

magnetic

s.

Apotentia

ldiff

erence

of

100

volt

sbetw

een

positiv

eand

negativ

esid

es

of

the

magnets

giv

es

a10

km

/svelo

city

whic

hshould

exis

tin

the

magnetiz

ed

regio

nofthe

pla

sm

a.

We

assum

ethatthere

will

be

avis

cous

coupling

of

the

magnetiz

ed

regio

nw

ith

the

unm

agnetiz

ed

regio

n.

The

peak

velo

city

UE×

B=

20

km

/s

isassum

ed

to

com

efr

om

a200

volt

diff

erence

betw

een

the

ele

ctrodes.

The

experim

ental

flexib

ility

of

the

rotatio

ncontrol

proposed

here

isrem

arkable

inthat

the

experim

enter

can

precis

ely

control

the

boundary

conditio

nΩ

(r

=a,

θ)by

adju

stin

gthe

volt

ages

betw

een

each

ofthe

ele

ctrodes.

So,fo

rexam

ple

,condit

ions

like

the

free-s

lip

surfa

ce

ofthe

sun

can

be

investig

ated

for

the

first

tim

e;at

the

equator

the

surfa

ce

of

the

sun

com

ple

tes

arotatio

nonce

every

25.4

days

while

near

the

pole

sit

’sas

much

as

36

days.

Rig

idrotatio

nshould

be

easy

to

accom

plish

by

adju

stm

ent

ofthe

ele

ctrode

voltages

at

each

latit

ude

to

impose

auniform

rotatio

n

rate

on

the

surfa

ce.

Assum

ing

that

the

magnets

are

uniform

lyseparated

polo

idally

and

that

they

have

identic

alstrengths,an

ele

ctrode

volt

age

∆U

(θ)∼

sin

θw

illgiv

euniform

rotatio

n.

One

mig

ht

ask

whether

more

com

ple

xflow

geom

etrie

sare

possib

lew

ith

such

asim

ple

flow

driv

e

or

ifthe

axis

ym

metric

geom

etry

preclu

des

more

com

plicated

flow

.T

he

flexib

ility

ofcontrollin

gthe

rotatio

nprofile

giv

es

aknob,how

ever,w

hic

hcan

be

used

to

driv

epolo

idalflow

s.

For

exam

ple

,ro-

tatin

gregio

nsnearthe

pole

sin

opposit

edir

ectio

ns,w

ith

rela

tiv

ely

little

rotatio

nnearthe

equatoria

l

regio

nis

exactly

the

type

ofgeom

etry

usin

gin

the

Von

Karm

an

flow

sregula

rly

investig

ated

influid

mechanic

sexperim

ents.

Inthose

experim

ents

dis

ks

at

each

end

ofa

cylindric

alvesselare

rotated

inopposit

edir

ectio

ns

makin

geach

hem

isphere

rotate

inopposit

edir

ectio

ns

and

strong

centrifugal

pum

pin

gthat

giv

es

polo

idalflow

sw

ith

inflow

at

the

equator

and

outflow

alo

ng

the

pole

s.

This

is

exactly

the

topolo

gy

used

inthe

liquid

sodiu

mversio

nofthe

Madis

on

Dynam

oE

xperim

ent

and

is

7

B

Arbitrary Vφ (r = a, θ)


33

MHD Computation Predicts Laminar Plasma Dynamo

Rm=300, Re=100

Te = 9 eV, n = 8 x1017 m-3

Umax = 5 km/s, Helium

3

5 10 15Time [!"]

10-12

10-10

10-8

10-6

10-4

10-2

Energ

y [arb

]

Velocity

Magnetic

FIG. 3: Energy versus time for the boundary condition givenin Figure 1. For this run Rm = 400.

0.0 0.5 1.0 1.5 2.0 2.5 3.0Angle [Radians]

-1.0

-0.5

0.0

0.5

1.0

Toro

idal S

peed [arb

]

FIG. 4: Toroidal boundary condition based on odd-numberedspherical harmonic components, ! = 1, 3, 5, 7.

spherical harmonic components, ! = 1, 3, 5, 7, is pre-sented in Figure 4. In contrast to the boundary con-dition presented in Figure 1, this boundary conditionhas several large-amplitude sign changes. The result-ing steady state velocity field is presented in Figure 5.This boundary condition generates much more flow thanthe previous example. Its poloidal flow is considerablystronger, and toroidal velocity field fills whole sphere.With such a stronger velocity field it comes as no sur-prise that Rmcrit = 280 for this flow, much lower thanthe previous example.

III. MRI SIMULATIONS

Dynamo physics is not the only physics accessible withsuch an experiment. Because the velocity field, to someextent, can be fine-tuned, many velocity fields which re-quire dedicated experiments to be generated can be pro-duced. For example, a boundary condition that followsa Keplerian profile is plotted in Figure 6. This boundarycondition is Keplerian (v! ! "!

3

2 , where " is the cylin-drical radial coordinate) in the range 0.3 " # " $ # 0.3.

-0.5 -0.2 0.0 0.2 0.5V [arb]

V# Vpol

t = 2.62!"

FIG. 5: Steady state velocity field generated by the toroidalboundary condition given in Figure 4, before the magneticfield energy becomes large. The plotting convention is thesame as in Figure 2.

0.0 0.5 1.0 1.5 2.0 2.5 3.0Angle [Radians]

0.0

0.2

0.4

0.6

0.8

1.0

Toro

idal V

elo

city [arb

]

FIG. 6: Toroidal boundary condition which follows a Keple-rian flow profile. Odd-numbered spherical harmonic compo-nents, ! = 1 ! 17, are used to generate this profile.

However, the flow generated by the boundary, presentedin Figure 7 with Rm = 300 and Pm = 1, is not Kep-lerian. To show this, Figure 7 presents the toroidal ve-locity field at the equator, as a function of radius. It isclear that v!

!

"2

"

! r!0.76 for much of the radial range.Nonetheless, the flow satisfies the conditions required tobe unstable to the MRI in much of the volume of thesphere15.

Part of the time evolution of the instability is presentedin Figure 9, wherein is plotted the energy in the domi-nant toroidal velocity field modes of the simulation, asa function of time, in resistive units. Initially no ex-ternal field is applied, and the dominant velocity field

Spence, Reuter, and Forest, A Spherical Plasma Dynamo Experiment, The Astrophysical Journal 700 470 (2009).

Toroidal Velocity Simulation Input

Toroidal

Poloidal


34

3000 4 kG SmCo Magnets Installed in MPDX



36

Current Setup

V! 0.0

+1.0

-1.0

North pole faces plasmaSouth pole faces plasma

LaB6 cathodeMolybdenum anode

90º N

90º S

0º

45º N

45º S

Coaxial LaB6 Cathode


37

Even without microwave heating, LaB6 stirring cathodes create hot, dense plasmas

Discharge powers of up to 20 kW result in ne= 5x1017 m-3, Te = 5 eV plasmas.

LaB6 cathodes draw up to 50A each during each 10 second plasma discharge.


38

Flow observed with cathodes withdrawn into magnetized region

Plasma spins up on neutral pump-out timescale.

3

(Te = 35 eV, Ti = 1 eV, Bcusp = 3000 G)

We = 2ρh = 4√ρeρi = 0.071 cm

1 >ωrf

Ωce=

ωrfme

eB

Re ∼ |(u·∇)u||ν∇2u| ∼ UL

ν

Rm ∼ |∇×(u×B)||λ∇2B| ∼ UL

λ = µ0σUL

∂B/∂t = ∇× (u×B) + λ∇2B

Pm = RmRe = µ0σν

Ro = U2LΩ sinφ

∂ω/∂t = ∇× (u× ω) + ν∇2ω

∂B

∂t= ∇× (u×B) + λ∇2B

mnduφdt

= (J×B)φ −mnuφτi0

+mnνii[∇2u]φ

τi0 =1

n0σcxu∂2uφ∂r2

+1

r

∂uφ∂r

−

1

L2u+

1

r2

uφ = 0

L2u = τi0νii

uφ(r) = AI1(r/Lu) +BK1(r/Lu)

Max velocity measured near anode location.Ve

loci

ty [

km/s

] fo

r Te=

5 eV

1

2

3

x1017

0

Neu

tral

Den

sity

[m-3]

1.0

0.8

0.6

0.4

0.2

Mach #

/ Ionization Fraction

Ionization Fraction

Ar Spin-Up at r=117 cm

Mach #n0

0 2 4 6 8 10 12 14 Time [s]

3

2

1

0

110 120 130 140 150 Radius [cm]

anode location

cathode location

Measured Velocity In Edge Region


39

Energy Balance (He)

0 20 40 60 80 100Te [eV]

1

10

100

kW

QtotQionizationQcuspQradQion radQei

density: 5.0E+17 m -35

Loss Mechanism Expression [Energy/Time]

Ion losses at cusps !Acusp(e"V + 3

2Ti)

Electron losses at cusps !Acusp( 32Te)

Replacement ionization Qioniz ! !AcuspEioniz

Neutral radiation M(Te)Qioniz

Charge-exchange collisions 3

2nn0"!cxv#e(Ti $ T0)V ol

Ion radiation n2Ri(Te)V ol

TABLE I. Power loss mechanisms in magnetic bucket. Acusp

is the e#ective loss area at the magnetic cusps; M(Te) is theradiation coe$cient for neutral radiation; n0 is the neutraldensity; !cx is the charge-exchange cross-section; V ol is theplasma volume; T0 is room temperature; and Ri(Te) is theion radiation coe$cient.

energy, but also the energy they gain as they fall throughthe potential di!erence between the plasma and the cusp(Eq. 2). This gained energy is much larger than the initialion thermal energy. The e!ective cusp area for plasmalosses, which is used in calculating ion power losses, isnot well-understood, and empirically is di!erent for fastelectrons and for bulk plasma species [12]; here, we takethe loss width to be 4

!!i!e, proportional to the geomet-

ric mean of the ion and electron gyroradii at the mag-net faces. As each ion is lost, we assume there mustbe a new ionization to replace it and keep the densityconstant; each ionization reduces the plasma’s stored en-ergy by Eioniz. Power may also be lost due to ion andneutral radiation. The radiation coe"cients associatedwith these processes, M(Te) and Ri(Te), were providedby Dennis Whyte using the KPRAD code [13].The procedure for energy balance is as follows: we start

with given density n and heating power and we calculateTe by setting the heating power equal to the sum of thepower losses listed in Table I. We neglect ion radiationand charge exchange losses, and we also ignore Ti in theexpression for ion losses at cusps since it is small relativeto e#V . The results for helium and argon are shownin Fig. 4 for two di!erent heating powers. Comparisonwith Fig. 3 shows that we must assume only a fraction ofthe heating power couples to the plasma. For example,in Fig. 3, at n = 7 " 1016 m!3, we measure Te = 5eV with 4 kW of heating power, similar to the powerbalance calculation with only 1 kW of heating power (seeFig. 4). In other words, if we assume that only 1/4 ofthe microwave power couples to the plasma, we are ableto account for the electron temperature.The ion temperature is more di"cult to model. Ion

power loss is given by the last two terms in Table I, whileions are heated by collisions with electrons and by thecombination of ion acceleration through #V and ion-ioncollisions in the edge region. This last heating mecha-nism is thought to be the dominant one, but it is notwell understood. Instead, we may estimate the ion tem-perature [8] to be 0.25-0.75 eV, consistent with previousmulticusp plasma experiments.The implications of this power balance calculation for

1016 1017 1018 1019100

101

102

n [m−3]

Te [e

V]

1kW 10kW

HeAr

FIG. 4. Power balance calculation for helium and argon with1 kW of heating power; electron temperature decreases withdensity. Argon has no solution above certain density becauseof large radiation power losses.

1016 1017 1018100

101

102

103

n [m−3]

v!=3 km/s, Ti=0.5 eV, PECH=1kW

Rm

Pm

Re

HeAr

FIG. 5. Power balance calculation of Rm, Re, and Pm asfunctions of density for 1 kW heating power; Rm uses electrontemperature from Fig. 4.

Re, Rm and Pm are shown graphically in Fig. 5. Wetake the case of 1 kW heating power and use the re-sults of Fig. 4. It is seen that Rm can reach 103 at lowdensities, a value much larger than in liquid metal exper-iments. In addition, Pm can now vary over a large range,as opposed to being fixed at # 10!6 as in liquid metals.With extra power, the magnetic Reynolds number is ex-pected to reach even higher values, as Te is increased.This scaling will be tested in an upcoming experiment,which has recently been constructed in Madison [14].

First Results

Make Predictions With Power Balance Calculations


40

Operational space set by power, density, and ion species

!"#$%&%' %&%( %&%)

*"+,-./012003

%

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41

Soon (May, 2013) … eventually (Fall, 2013)

V! 0.0

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90º N

90º S

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45º S

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90º N

90º S

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45º S


42

Summary

•Controlled velocity profiles can be created in axisymmetric ring cusp geometry using biased cathodes in the magnetized edge to drive flows in the bulk, unmagnetized plasma

•Within a factor of Ti, the measured viscosity is consistent with Braginskii

•Rotation at the inner boundary has recently been achieved in PCX, which now allows us to explore hydrodynamic and magnetohydrodynamic stability

•MPDX is entering final phase of construction, expected to achieve Rm ~1000


43

Further Reading

Stirring Unmagnetized Plasma C. Collins et al., Phys. Rev. Lett. 108, 115001 (2012).

Magnetic Bucket for Rotating Unmagnetized PlasmaN. Katz et al., Rev. Sci. Instrum. 83, 063502 (2012).

Global Hall-MHD Simulations of MRI in a Plasma Couette Flow Experiment F. Ebrahimi, et al., Phys. Plasmas 18, 062904 (2011).

Numerical Simulation of Laminar Plasma Dynamos in a Cylindrical Von Kármán FlowKhalzov, et al., Phys. Plasmas 18, 032110 (2011).

A Spherical Plasma Dynamo ExperimentSpence, Reuter, and Forest, The Astrophysical Journal 700, 470 (2009).

Resistive and Ferritic-Wall Plasma Dynamos in a SphereKhalzov, et al., Phys. Plasmas 19, 104501 (2012).

Optimized Boundary Driven Flows for Dynamos in a SphereKhalzov, et al., Phys. Plasmas 19, 112106 (2012).

PCX

MPDX


44

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Pm=2.1, α=6, ν=134

Pm=1.3, α=8, ν=90

n=2.5x1010 cm-3, Te=7 eV, Ti=.3 eV

n=2.4x1010 cm-3 , Te=6.5 eV , Ti=.25 eV

n=5x1010 cm-3, Te=6.3 eV, Ti=.25 eV

Helium, P=1x10-4 Torr

Pm=0.6, α=10 ,ν=44

The Goal: Achieve MRI Unstable Parameters

MRI stable region

Rayleigh line

MRI Could Be Unstable At Feasible Parameters


45



How Close Are We To MRI Instability?

-Still need to turn on the Bz field (may change filament placement)-MRI analysis is local



47

Taylor Vortices Can Occur at High Vinner, Low Viscosity

-Marginal stability analysis is local-What are the boundary conditions?

unstable

stable


48

Ti = 0.058 ± 0.0026 eV

Doppler Broadening Doppler Shiftλ0 = 1047.00475

Ti = 0.5 eV Vi = 5 km/s∆λ=0.009 nm 0.0175 nm

Preliminary LIF Temperature Measurements


49

1700°C

~3 cm from magnet

Magnet Temperature (Front & Back)

Before After

Center Stack Temperature Reduced By Silvering


50

Particle Balance

Vplasma = 10 m3

Aloss = Wcusp × Lcusp

Wcusp = 4√ρeρi ∼ 1 mm

Lcusp = 220 m

dndt = 1

2csnAlossVplasma


Documents

Spinning an Unmagnetized Plasma for Magnetorotational and ...kunz/Site/PCTS_files/Modeling rot… · 23 Helium V o=6.5 km/s, n=2x1018 m-3, T e=8 eV, T i=1.5 eV, F. Ebrahimi, 2011