xb configurations for lasma ass

EXB CONFIGURATIONS FOR PLASMA MASS SEPARATION

EXB WORKSHOP - PRINCETON - NOV. 1ST/2ND 2018 ROTATING PLASMAS

RENAUD GUEROULT

LABORATOIRE PLASMA ET CONVERSION D’ENERGIE (LAPLACE), CNRS, TOULOUSE, FRANCE

in collaboration with

J.-M. RAX UNIVERSITÉ DE PARIS XI - ECOLE POLYTECHNIQUE, LOA-ENSTA-CNRS, PALAISEAU, FRANCE

N. J. FISCH, S. J. ZWEBEN, I. E. OCHS, F. LEVINTON PRINCETON PLASMA PHYSICS LABORATORY, PRINCETON NJ, USA

R. Gueroult | ExB Workshop Princeton | Nov. 2018

NEW NEEDS FOR MASS SEPARATION AT ELEMENTAL LEVEL

NdFeB magnets recycling.

Spent nuclear fuel reprocessing

Nuclear waste cleanup


MASS SEPARATION AT THE ELEMENTAL LEVEL

Aug. 12, 1958 E. o. LAWRENCE ‘ 2,847,576 ' CALUTRON SYSTEM

Filed Jan. 16, 1946 , - 2 Sheets-Sheet 1

‘a INVENTOR _. ' [RA/£57 0 LAWRENCE

Fa?! BYr %‘ ATTORNEY

Mass separation at the elemental level was initially driven by isotope separation. Plasma separation was developed in this context.


MASS SEPARATION AT THE ELEMENTAL LEVEL

Aug. 12, 1958 E. o. LAWRENCE ‘ 2,847,576 ' CALUTRON SYSTEM

Filed Jan. 16, 1946 , - 2 Sheets-Sheet 1

‘a INVENTOR _. ' [RA/£57 0 LAWRENCE

Fa?! BYr %‘ ATTORNEY

Mass separation at the elemental level was initially driven by isotope separation. Plasma separation was developed in this context.

⇠ 1 amu ⇠ 30� 50 amu

10 kg/year 10 T/year

New needs require new solutions for at least two reasons:

Large mass differences

High throughput


EXB FLOW IN UNIFORM MAGNETIC FIELDMass di↵erential e↵ects in magnetized rotating plasmas for separation applications 5

Figure 2. Linear configuration: uniform axial magnetic fieldand radial electric field.

Considering the plasma column in Fig. 2, andneglecting first collisions, the radial force balance ona particle of charge q and mass m writes

�!

2 =q

mr

Er + sgn(q)⌦!, (1)

with ! the particle azimuthal angular frequency,sgn(x) = x/|x| the sign function and ⌦ = |q|B0/m

the cyclotron frequency. The equilibrium solution isdescribed by the slow and fast Brillouin modes [60]

!B± = �sgn(q)

⌦

2

"1±

s

1� 4mEr

qB02r

#. (2)

Out of these two modes, only the slow mode !B�

depicted in Fig. 3 arises spontaneously. Introducingthe azimuthal drift velocity in the limit of zero inertia⌦E = �Er/(rB0), Eq. (2) rewrites

!B� = �sgn(q)

⌦

2

"1�

r1 + 4sgn(q)

⌦E

⌦

#. (3)

Taylor expanding Eq. (3) for |⌦E |/⌦ ⌧ 1, one gets

!B� = ⌦E

"1� sgn(q)

⌦E

⌦+O

⌦E

⌦

�2!#(4)

In the limit |⌦E |/⌦ ! 0, one recovers ! = ⌦E . In thislimit, there is no di↵erence in azimuthal E ⇥ B driftvelocity between charged species.

For Er 0, ⌦E � 0, and plasma rotation is inthe counter-clockwise direction. Eq. (3) shows thatcentrifugal e↵ects speed up rotation for negativelycharged particles, and slow up particles for positivelycharged particles, as seen in Fig. 3. For two positiveions of di↵erent mass, the angular velocity of thelight ion is larger than the angular velocity of theheavy ion. On the other hand, rotation is in theclockwise direction for Er � 0, and ⌦E 0. For

-0.2 -0.1 0 0.1 0.2

-0.4

-0.2

0

0.2

0.4

Figure 3. Slow Brillouin mode for positively (blue) andnegatively (red) charged particles, with ⌦ = |q|B0/m the gyro-frequency and ⌦E = �Er/B0 the E⇥B drift angular frequency.Rotation is counter-clockwise (!B

� > 0) for Er < 0, andreciprocally. The black dotted curve represents the zero inertiasolution.

this polarity, positively charged particles rotate faster,while negatively charged particles rotate slower. Fortwo positive ions of di↵erent mass, the norm of theangular velocity of the light ion is smaller than thenorm of the angular velocity of the heavy ion. Notethat the di↵erence in azimuthal velocity between twodi↵erent ion species leads to a positive (resp. negative)azimuthal drag force on heavy (resp. light) ionsno matter the polarity of the radial electric field.In both cases, this drag force causes light ions todrift radially inward and heavy ions to drift radiallyoutward. This is the physical mechanism behindplasma centrifugation [11].

Now, looking at Eq. (3), one notices that there isno solution if

sgn(q)⌦E

⌦� �1/4. (5)

This limit, known as the Brillouin limit, means thations are radially unconfined for fast enough rotation inthe clockwise direction, and electrons are unconfinedfor fast enough rotation in the counter-clockwisedirection. Since ⌦e � ⌦i, the latter is howeverunlikely.

To illustrate these confinement properties, it isinteresting (as it will become clear later) to considerparticle equilibrium in the frame rotating with theangular velocity $ = �sgn(q)⌦/2 e

z

. Let us denotevariables in this rotating frame with a . Since@$/@t = 0, the fields transformation reads

E = E+ ($ ⇥ r)⇥B (6a)

B = B. (6b)

!B� = �sgn(q)

⌦

2

"1�

r1 + 4sgn(q)

⌦E

⌦

#

!|⌦E |⌧⌦

⌦E

In a crossed field configuration with axial Bz field

and radial Er field, centrifugal forces create an addi-

tional drift. The angular frequency is not Er/(Bzr).

with ⌦ = |q|B0/m and ⌦E = �Er/(rB0).


EXB FLOW IN UNIFORM MAGNETIC FIELDMass di↵erential e↵ects in magnetized rotating plasmas for separation applications 5



�!

2 =q

mr

Er + sgn(q)⌦!, (1)



!B± = �sgn(q)

⌦

2

"1±

s

1� 4mEr

qB02r

#. (2)



!B� = �sgn(q)

⌦

2

"1�

r1 + 4sgn(q)

⌦E

⌦

#. (3)


!B� = ⌦E

"1� sgn(q)

⌦E

⌦+O

⌦E

⌦

�2!#(4)



-0.2 -0.1 0 0.1 0.2

-0.4

-0.2

0

0.2

0.4





sgn(q)⌦E

⌦� �1/4. (5)



z


E = E+ ($ ⇥ r)⇥B (6a)

B = B. (6b)

!B� = �sgn(q)

⌦

2

"1�

r1 + 4sgn(q)

⌦E

⌦

#

!|⌦E |⌧⌦

⌦E

In a crossed field configuration with axial Bz field

and radial Er field, centrifugal forces create an addi-

tional drift. The angular frequency is not Er/(Bzr).

with ⌦ = |q|B0/m and ⌦E = �Er/(rB0).

Mass di↵erential e↵ects in magnetized rotating plasmas for separation applications 5



�!

2 =q

mr

Er + sgn(q)⌦!, (1)



!B± = �sgn(q)

⌦

2

"1±

s

1� 4mEr

qB02r

#. (2)



!B� = �sgn(q)

⌦

2

"1�

r1 + 4sgn(q)

⌦E

⌦

#. (3)


!B� = ⌦E

"1� sgn(q)

⌦E

⌦+O

⌦E

⌦

�2!#(4)



-0.2 -0.1 0 0.1 0.2

-0.4

-0.2

0

0.2

0.4





sgn(q)⌦E

⌦� �1/4. (5)



z


E = E+ ($ ⇥ r)⇥B (6a)

B = B. (6b)

Centrifugal forces accelerate rotation for

sgn(q)⌦E < 0, and slow down rotation for

sgn(q)⌦E > 0.

If sgn(q)⌦E⌦ � �1/4, there is no radial con-

finement.


EXB FLOW IN UNIFORM MAGNETIC FIELD (2)

Another way to look at this is through the e↵ective po-

tential in the rotating frame where the magnetic field

cancels,

�?(r) = �(r) +

qB02

8mr2

with �(r) the electric potential applied in the lab frame.

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Centrifugal + Coriolis




Assuming the fields in the rotating frame do notdepend on time, one can rewrite the Newton-Lorentzequation as (see for example, Ref [61, p. 328])

m

@v

@t

= q(E? + v ⇥B

?) (7)

with

E

? = E+r✓m$

2r

2

2q

◆(8a)

B

? = B+2m

q

$ = 0. (8b)

Eq. (8b) shows that in the chosen frame rotatingwith the angular frequency $ = �sgn(q)⌦/2 e

z

, themagnetic field cancels. In this frame, the particledynamics is only controlled by the electric field E

?.The second term on the right hand side in Eq. (8a) isthe contribution of the centrifugal force. Introducingthe e↵ective potential

�

?(r) = �(r) + [2sgn(q)� 1]qB0

2

8mr

2, (9)

Eq. (8a) writes E

? = �r�

?. Since the Coriolisforce is proportional to $, it depends on the signof the rotation and therefore here on the sign ofthe particle charge. In contrast, the centrifugalforce is proportional to $

2, and is therefore positiveirrespective of the sign of the particle charge. Forpositively charged particles, Coriolis and centrifugalforces are in opposite direction, and one gets

�

?(r) = �(r) +qB0

2

8mr

2. (10)

If the potential applied in the laboratory frameis constant (@�/@r = 0), the e↵ective potential �? inEq. (10) is convex, and ions are confined. Eq. (9) showselectrons are also confined in this case. Now assume aparabolic potential profile �(r) = ↵r

2 is applied in thelaboratory frame. This corresponds to a solid bodyrotating plasma column since Er / r so @⌦e/@r = 0,and thus, using Eq. (3), @!B

�/@r = 0. For ↵ �

�qB02/(8m), an ion of mass m and charge q is still

confined. On the other hand, for ↵ �qB02/(8m),

Eq. (10) tells us that �

? is concave. An ion of massm and charge q is therefore radially unconfined. Thechange in concavity of the e↵ective potential profile�

?(r) is illustrated in Fig. 4. The threshold value↵c = �qB0

2/(8m) for ion confinement can be rewritten

Er/(rB0) = ⌦/4, which is the Brillouin limit given inEq. (5). Now suppose a multi-ion species plasma with↵ = �qB0

2/(8m⇧), so that

�

?(r) =qB0

2

8mm⇧(m⇧ �m)r2. (11)

The e↵ective potential �

? indicates that a singlycharged ion with mass m � m⇧ will be radiallyunconfined, while a singly charged ion with mass m

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

2nd order

(a) Laboratory potential �(r)

0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

1.4

1.5

2nd order, 80 amu2nd order, 120 amu

(b) E↵ective potential �?(r)

Figure 4. Applied laboratory potential radial profile �(r)[(a)] and e↵ective potential radial profile �?(r) for two di↵erention mass [(b)]. Solid line curves are obtained for �(r) =Va(1 � r2/a2), while dotted line curves are obtained for �(r) =�r4+Va(1�r2/a2), � 2 IR. Va is the potential di↵erence acrossthe plasma column for the parabolic case, a is the plasma columnradius. The addition of a fourth order term to the parabolicprofile leads to the formation of a potential well o↵-axis for heavyions (dotted blue curve).

m⇧ will be radially confined. This charge to mass ratiothreshold for confinement is the basis for the DC bandgap ion mass filter [62] used in the Archimedes plasmamass filter [63]. In this device, ions are separated intotwo components: light ions m/m⇧ < 1 are collectedaxially along the magnetic field lines while heavy ionsm/m⇧ > 1 are collected radially.

Practically, this filtering mechanism has a fewlimitations. First, since the confinement criteriadepends on the charge to mass ratio and not on themass alone: a doubly charged ion of mass 2m can notbe di↵erentiated from a singly charged ion of mass m.

Take a parabolic profile �(r) = ↵(1 � r2) (solid body

rotation), and write ↵ = qB02/(8m⇧

). Then

�?=

qB02

8mm⇧ (m⇧�m)r2 ,! Light ions confined

heavy ions unconfined

<latexit sha1_base64="rxAqpEf3wvGOkr+A2VYg9dCyUiA=">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</latexit><latexit sha1_base64="rxAqpEf3wvGOkr+A2VYg9dCyUiA=">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</latexit><latexit sha1_base64="rxAqpEf3wvGOkr+A2VYg9dCyUiA=">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</latexit><latexit sha1_base64="rxAqpEf3wvGOkr+A2VYg9dCyUiA=">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</latexit>



cancels,

�?(r) = �(r) +

qB02

8mr2






Higher order potential profile in the lab frame can beused to create wells in e↵ective potential. The well radialposition depends on the ion mass.



m

@v

@t

= q(E? + v ⇥B

?) (7)

with

E

? = E+r✓m$

2r

2

2q

◆(8a)

B

? = B+2m

q

$ = 0. (8b)


z



�

?(r) = �(r) + [2sgn(q)� 1]qB0

2

8mr

2, (9)

Eq. (8a) writes E

? = �r�



�

?(r) = �(r) +qB0

2

8mr

2. (10)



�/@r = 0. For ↵ �








2/(8m⇧), so that

�

?(r) =qB0

2

8mm⇧(m⇧ �m)r2. (11)



0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

2nd order4th order


0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

1.4

1.5

2nd order, 80 amu2nd order, 120 amu4th order, 80 amu4th order, 120 amu





Take a parabolic profile �(r) = ↵(1 � r2) (solid body

rotation), and write ↵ = qB02/(8m⇧

). Then

�?=

qB02

8mm⇧ (m⇧�m)r2 ,! Light ions confined

heavy ions unconfined

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cancels,

�?(r) = �(r) +

qB02

8mr2





EXB SEPARATORS IN UNIFORM AXIAL MAGNETIC FIELD



m

@v

@t

= q(E? + v ⇥B

?) (7)

with

E

? = E+r✓m$

2r

2

2q

◆(8a)

B

? = B+2m

q

$ = 0. (8b)


z



�

?(r) = �(r) + [2sgn(q)� 1]qB0

2

8mr

2, (9)

Eq. (8a) writes E

? = �r�



�

?(r) = �(r) +qB0

2

8mr

2. (10)



�/@r = 0. For ↵ �








2/(8m⇧), so that

�

?(r) =qB0

2

8mm⇧(m⇧ �m)r2. (11)



0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

2nd order


0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

1.4

1.5

2nd order, 80 amu2nd order, 120 amu





Axial - radial separation in parabolic profile Solid body rotation

Ohkawa and Miller (2002), Phys. Plasmas, 9, 5116


EXB SEPARATORS IN UNIFORM AXIAL MAGNETIC FIELD

Axial - radial separation in parabolic profile Solid body rotation

Ohkawa and Miller (2002), Phys. Plasmas, 9, 5116



m

@v

@t

= q(E? + v ⇥B

?) (7)

with

E

? = E+r✓m$

2r

2

2q

◆(8a)

B

? = B+2m

q

$ = 0. (8b)


z



�

?(r) = �(r) + [2sgn(q)� 1]qB0

2

8mr

2, (9)

Eq. (8a) writes E

? = �r�



�

?(r) = �(r) +qB0

2

8mr

2. (10)



�/@r = 0. For ↵ �








2/(8m⇧), so that

�

?(r) =qB0

2

8mm⇧(m⇧ �m)r2. (11)



0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

2nd order4th order


0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

1.4

1.5

2nd order, 80 amu2nd order, 120 amu4th order, 80 amu4th order, 120 amu





Axial - Axial separation with a 4th order potential Sheared rotation

Gueroult et al. (2014), Phys. Plasmas, 21, 02070


Light elements

Heavy elements

Rotation axis

Magnetic field line

Ion mixture

Figure 3. Linear configuration: uniform axial magnetic field and radial electric field.

-0.2 -0.1 0 0.1 0.2

-0.4

-0.2

0

0.2

0.4



of the rotation and therefore here on the sign ofthe particle charge. In contrast, the centrifugalforce is proportional to $


�

?(r) = �(r) +qB0

2

8mr

2. (10)



�/@r = 0. For ↵ �




? is concave. An ion of mass

m and charge q is therefore radially unconfined. Thechange in concavity of the e↵ective potential profile�




2/(8m⇧), so that

�

?(r) =qB0

2

8mm⇧(m⇧ �m)r2. (11)


? indicates that a singlycharged ion with mass m � m⇧ will be radiallyunconfined, while a singly charged ion with mass m m⇧ will be radially confined. This charge to mass ratiothreshold for confinement is the basis for the DC bandgap ion mass filter [62] used in the Archimedes plasmamass filter [63]. In this device, ions are separated intotwo components: light ions m/m⇧ < 1 are collectedaxially along the magnetic field lines while heavy ionsm/m⇧ > 1 are collected radially.

Practically, this filtering mechanism has a fewlimitations. First, since the confinement criteriadepends on the charge to mass ratio and not on themass alone: a doubly charged ion of mass 2m can notbe di↵erentiated from a singly charged ion of mass m.This means that heavy doubly charged ions will becollected with light singly charged ions. Second, thefiltering mechanism relies on low collisionality, whichsets a limit on plasma density and hence throughputfor a given magnetic field intensity. Indeed, theradial ion transport induced by collisions with neutralsbrings light ions (m/m⇧ < 1) to the heavy ions(m/m⇧ > 1) stream. Strictly speaking, ion-neutralcollisions slow down the slow mode and suppressthe requirement for ion radial confinement ⌦E/⌦ ��1/4 [64]. In other words, the Brillouin limit breaksdown. Separation then hinges on the di↵erential radialtransport properties of light and heavy ions. Finally,and maybe most importantly, another limitation isthat heavy ions are typically collected over a largeregion of the plasma chamber. This is because heavyions are extracted perpendicularly to the field lines


WHAT HAPPENS IN A MORE GENERAL FIELD Brer +Bzez

Heavy

Light

Iso-rotation states ⌦ = cst along a field line.

,! there is a centrifugal potential barrier

m⌦

2(r2 � rm2

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Gueroult et al. (2018), Plasma Phys. Controlled Fusion, 60, 014018



Heavy

Light



m⌦

2(r2 � rm2


vk2 (r⌦)2

✓1� rM 2

r2

◆+ v?

2

✓BM

B� 1

◆

<latexit sha1_base64="xcTDcOnrKij/6gS8caTZ5qMZz9c=">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</latexit><latexit sha1_base64="xcTDcOnrKij/6gS8caTZ5qMZz9c=">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</latexit><latexit sha1_base64="xcTDcOnrKij/6gS8caTZ5qMZz9c=">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</latexit>

Rotation

Rotating mirror: enhanced confinement

loss “cone” ↘ m

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Heavy

Light



m⌦

2(r2 � rm2


vk2 (r⌦)2

✓1� rM 2

r2

◆+ v?

2

✓BM

B� 1

◆

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Rotation

Rotating mirror: enhanced confinement

loss “cone” ↘ m

Separation: degraded confinement

loss “cone” m

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EXB SEPARATOR IN ASYMMETRIC GEOMETRY

Axial - Axial separation in an symmetric rotating plasma The Magnetic Centrifugal Mass Filter

Fetterman and Fisch (2011), Phys. Plasmas, 18, 094503 Gueroult and Fisch (2012), Phys. Plasmas, 19, 122503


NUMERICAL VALIDATION: DIFFERENTIAL CONFINEMENT IN THE MCMF

Preliminary estimates for separation efficiencies in the MCMF device

Magnetic field map used as a simulation input, and ion (144 amu) trajectory in the 3D field with collisions (241Am).

ne = ni = 1.5 1012 cm�3

Ti = 20 eV, Te = 2 eV, vE⇥B = 8.5km. s�1


KEY CHALLENGES AND OPEN QUESTIONS

Rotating, and more generally crossed-field, plasma configurations are only a subset of the many options plasmas offer for mass separation. Yet, these concepts already reveal a common set of scientific and technological challenges. To name a few:

Zweben, Gueroult and Fisch (2018), Phys. Plasmas, 25, 090901




Separation is generally based on the ion charge to mass ratio Ze/m

→ Need to get as close as possible to uniform charge state, which is challenging in mixtures.







For each filter concept, separation is conditioned upon a suitable collisionality regime

→ Need to control plasma parameters, in particular neutral and plasma densities and Ti.





n Ti Te E

1013 cm-3 10-100 eV 1-5 eV 20 V/cm



For each filter concept, separation is conditioned upon a suitable collisionality regime

→ Need to control plasma parameters, in particular neutral and plasma densities and Ti.

Each ExB filter concept requires a particular perpendicular electric field

→ Need to control the perpendicular electric field for plasma parameters derived from other constraints.



ECR RESULTS

VoLUME 56, NUMsm 17 PHYSICAL REVIEW LETTERS 28 APR.rL 1986

dependently, where QT(n/P/y) represents that thebias potentials of the inner, middle, and outer elec-trodes are u, P, and y V, respectively. Small movableLangmuir probes, which can be also used as emissiveprobes, are inserted radially and axially to measure theplasma parameters and their fluctuations.When all of the segmented electrodes are grounded,

axial and radial profiles of the plasma density n aremeasured as shown in Fig. 2. Around the mirrorcenter, n = 3 && 10" cm 3, electron temperatureT, = 5 eV, and ion temperature T; & 1 eV. Appreci-able spatial variations of T, and T, are not recognized.The plasma potential @ is observed to change slightlyin the range less than or approximately a few voltsalong the magnetic field. In Fig. 2, the plasma isfound to be well trapped in the mirror field, beingbounded by the magnetic field lines which intersectthe chamber wall at the mirror midplane. Even if allof the segmented electrodes are floated (floating po-tentials are 1.3, 1.3, and 3.5 V for the inner, middle,and outer electrodes, respectively), the profiles of nare almost the same as in Fig. 2.

In order to change a radial profile of plasma poten-tial tt), different bias potentials are applied to the seg-mented electrodes. Figure 3 demonstrates typical ex-amples of controlled radial potential profiles and corre-sponding density profiles around the mirror midplane.Here the segmented electrodes are biased in the sameway at both ends. Hill- and well-shaped potential pro-files are found to be successfully formed. The hill-shaped potential profile is formed when the segmentedelectrodes are biased in the way n )P & y. On theother hand, the well-shaped profile is formed by theopposite combination of the bias potentials, i.e. ,a & P ( y. A gradual change of the potential profile isobserved between the hill- and well-shaped profiles.Even near the chamber wall, the plasma potentialdepends on the potential applied to the segmentedelectrodes. It must be remarked that o. , P, and y are

3 ywa

1 8V

2

p . I I I I I I I

EAST 6O QG 20 0 20 QO 60 HEST

z (cm)

Q(20/0/-2 0)(15/0/-15)

(10/0/-10)(5/0/-5)/0))

10

20 & --'r I 1 I rI ~ I

f- --- j- (0/0(-5/0/5

(-10/0/10)I. (-15/0/15)

(-20/0/20)

r (em)

FIG. 2. Axial and radial profiles of plasma density n w'henall segmented electrodes are grounded electrically. Mi-crowave po~er =500%. Ar gas pressure =5x10 5 Torr.Solid lines are obtained by measurement of ion saturationcurrents of Langmuir probes. Open circles show the valuesobtained from the characteristics of Langmuir probes. A, 8,C, and D correspond to the positions of the probes in Fig.1(a).

+20/0/-20)(15/0/-], 5)0/-10)8 /

CD LI

L-(-15/0/15)

(-20/0/20)0 10r (cm)

FIG. 3. (a) Controlled radial profiles of plasma potentialand (b) corresponding profiles of plasma density n

$T a/P/y) represents that bias potentials of inner, middle,and outer electrodes are u, P, and y V, respectively.

Tsushima et al. (1986), Phys. Rev. Lett., 56, 1815

Successful in creating positive and negative electric field using three ring electrodes in an

ECR plasma in mirror geometry.

n Ti Te E

~1/50 ~1/100 ~1 ~1/10

Relative to values targeted for separation

xb configurations for lasma ass

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