design of pm helicon arrays

Design of PM helicon arrays

UCLA

1. Optimization of the discharge tube

2. Design of the permanent magnets

3. Design of a multi-tube array

4. Design and construction of a test chamber

5. Antennas and the RF distribution system

6. Experimental results

7. Design of a compact module

8. Ideas for further improvements to be tested

A commercial helicon etcher (PMT MØRI)

It required two heavy electromagnets with opposite currents.

Previous experiment with 7 tubes

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ROTATING PROBE ARRAY

PERMANENT MAGNETS

3"

DC MAGNET COIL

18"

54 mm

2.4 mm

6.4 mm10 cm

2.5

cm

The “stubby” tube

It required a large electromagnet

Plasmas merged; density is uniform

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Power scan at z = 7 cm, 5 mT A, 20 G, 13.56 MHz,

0.0

0.5

1.0

1.5

2.0

0 5 10 15 20 25 30R (cm)

N (

101

2 cm

-3) 3.0

2.5

2.0

1.5

1.0

P(kW)

7-tube m=0 array

ARGON

High density and uniformity were achieved

A c o m p u t a t i o n a l p r o g r a m f o rH E L I C O N s a n d I C P s

V e r s i o n 1 . 0

A u t h o r : D o n a l d A r n u s h , w i t h F r a n c i s F . C h e nP r o g r a m m e r s : R i c k L a n , R a v a s h E l i a s s i

U C L AA

Optimization of discharge tube: HELIC code

UCLAD. Arnush, Phys. Plasmas 7, 3042 (2000).

Radial profiles are arbitrary, but B and n must be uniform axially.

HELIC gives not only the wave fields but also R, the loading resistance.

a

b

c

AntennaLc

a b

h

Loop antenna

Helical antenna

B0

The HELIC user interface

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The Low-field Peak

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DENSITY vs. MAGNETIC FIELD4-cm tube, uniform field

0.0

0.5

1.0

1.5

2.0

0 20 40 60 80 100 120B (G)

n (1

012

cm

-3)

Mechanism of the Low Field Peak

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0 1,r

z

ne nk

k B a k B

Basic helicon relations

The peak is sensitive to the density profile

0

1

2

3

4

5

6

0 50 100 150 200 250 300

B (G)

R (

ohm

s)

Uniform

Flat with rolloff

Parabolic

The peak depends on the boundary condition

0

1

2

3

4

5

6

7

8

0 50 100 150 200 250 300

B (G)

R (

ohm

s)

Insulating

Conducting

The peak depends on distance from endplate

0

1

2

3

4

5

6

0 50 100 150 200 250 300

B (G)

R (

ohm

s)

5 cm

10 cm

No bdy

d

The peak depends on the type of antenna

0

1

2

3

4

5

6

0 50 100 150 200 250 300

B (G)

R (

ohm

s)Loop, d = 10 cm

HH10, d = 10 cm

Nagoya III

Single loop: m = 0, bidirectionalHH (half-wavelength helical): m = 1, undirectionalNagoya Type III: m = 1, bidirectional

Typical scan of Rp vs n, B

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0.0

0.5

1.0

1.5

2.0

2.5

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

1000464215100462210

B (G) d = 3", H = 2", 13.56MHz

Each point requires solving a 4th order differential equation >100 times.A typical scan takes ~ 3 hours on a PC.

Matrices for optimizing discharge tube

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Vary the tube length and diameter Vary the RF frequency

Vary the pressure and frequency

Vary the endplate conductivity

Vary H (endplate distance) for 3” diam

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0.0

0.5

1.0

1.5

2.0

2.5

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

H = 3 in.

H = 2 in.

H = 1 in.

100G, d = 3", 13.56 MHz

Vary diam for H = 2” at 100G

UCLA

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

d = 4 in.

d = 3 in.

d = 2 in.

100G, H = 2", 13.56 MHzTube diameter

Vary the frequency

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

f = 27.12 MHz

f = 13.56 MHz

f = 2 MHz

D = 3", L = 2", 100G

Not much variation with pressure

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0.0

0.5

1.0

1.5

2.0

2.5

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

1 mTorr

3 mTorr10 mTorr

D = 2", H = 1.5", 100G

Vary the endplate material

UCLA

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

Conducting

Insulating

H = 2", D = 2", B = 80G

0.0

0.2

0.4

0.6

0.8

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

H = 1.5 in., conducting

H = 3.0 in., insulating

Initially, it seems that the conducting endplate is better. However, it is because the phase reversal at the endplate has changed, and the tube length has to be ~1/4 wavelength longer to get constructive interference. By changing H, almost the same R can be achieved.

Relation of R to plasma density

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pin rf

p c

RP P

R R

7 1/ ½ 1.0 10 secsdN dt Snc n

c i eW E W W 101.1 10 WattsoutP n

Rp << Rc

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1E+11 1E+12 1E+13n (cm-3

)

R (

oh

ms)

100 G

63 G

40 G

25 G

16 G10 G

Relation of R to plasma density

UCLA

pin rf

p c

RP P

R R

7 1/ ½ 1.0 10 secsdN dt Snc n

c i eW E W W 101.1 10 WattsoutP n

10

100

1000

1E+11 1E+12 1E+13n (cm-3)

Pin

(W

)1000

500

200

100

Loss

Prf (W)

Rp > Rc

Final design

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2.120.25

4.00

2.25

Lesker QF50 cover plate

Lesker QF50 centering ringParker 2-330 Viton O-ring

Corning #237580 tubing, 63.5 mm OD, 4.8 mm wall

Parker 2-239 Viton O-ring

Dimensions are in inches

The “New Stubby” tube

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Characteristics of permanent magnet rings

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Internal field

External field

The B-field of annular PMs

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The field reverses at a stagnation point very close to the magnet.

Plasma created inside the rings follows the field lines and cannot be ejected.

Optimization of magnet geometry

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Result: Field strength magnet volumeSpacing improves uniformity slightly

actual

actual

The field of 4 stacked magnet rings

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-400

-300

-200

-100

0

100

200

-20 -15 -10 -5 0 5 10 15 20z (cm)

Bz

(G)

0.0

2.5

4.0

r (cm)

0

50

100

150

200

250

300

-20 -15 -10 -5 0 5 10 15 20z (cm)

|Bz|

(G

)

Calc.

Expt.

The internal and external fields at various radii. The individual rings can be seen at large radii.

Calibration of the calculated field with a gaussmeter.

For the designed tube, B ~ 60G is good

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1E+11 1E+12 1E+13n (cm-3)

R (

oh

ms)

100.0

63.1

39.8

25.1

15.8

10.0

B(G) L=2", 1mTorr, conducting

Proof of principle on 3” diam tube

UCLA

Gate Valve

To Turbo Pump

34 cm

36 cm

D

Z1

Z2

0

20

40

60

80

100

120

5 10 15 20 25 30 35 40z (cm)

Bz

(G)

B (0)231928

3338

D (cm)

-300

-250

-200

-150

-100

-50

0

50

100

150

0 5 10 15 20 25 30

z (cm)

Bz

(G)

Calculated

Measured

External field

Internal field

Radial density profiles at Z1 and Z2

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0

2

4

6

8

10

-5 0 5 10 15 20r (cm)

n (

101

0cm

-3)

Z1, 40

Z1, 35

Z1, 30

Z1, 21

Z1, 1

D (cm)500W, 1mTorr

0

1

2

3

4

5

6

7

-5 0 5 10 15 20r (cm)

n (

101

0cm

-3)

Z2, 40

Z2, 35

Z2, 30

Z2, 21

Z2, 1

D (cm)

500W, 1 mTorr

Upper probe Lower probex 1010 cm-3

Proof of principle: discharge in the external field gives much more plasma downstream.

The final design for 2” tubes

UCLA

12.7 cm

7.6 cm

PLASMA

Material: NdFeB

Bmax = 12 kG

Attractive force between two magnets 2 cm apart:

516 Newtons = 53 kg

The magnets are dangerous!

Wooden frame for safe storage

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Single tube, final configuration

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0

50

100

150

200

250

300

350

-4 -2 0 2 4r (cm)

Bz

(G)

56789101214

z (cm from midplane of magnet)

Radial Bz profiles at various distances below the magnet.

Discharge tube


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Design of array

UCLA

The density at Z2 is summed over nearest tubes.

0

2

4

6

8

10

-5 0 5 10 15 20r (cm)

n (

10

11cm

-3)

Z1, single magnet

Z1, with neighbors

Z2, single magnet

Z2, with neighbors Radial density profilesat Z1 = 7.4 cm and Z2 = 17.6 cm below discharge.

Computed uniformity n(x) for various y

0

1

2

3

4

5

6

7

8

-30 -20 -10 0 10 20 30x (cm)

n (

10

11 c

m-3

)

Sum

Row1

Row2

Avg: all y

y = 0

(a)

0

1

2

3

4

5

6

7

8

-30 -20 -10 0 10 20 30x (cm)

n (

10

11 c

m-3

)

Sum

Row1

Row2

Avg: all y

y = 7.5

(b)

0

1

2

3

4

5

6

7

8

-30 -20 -10 0 10 20 30x (cm)

n (

10

11 c

m-3

)

Sum

Row1

Row2

Avg: all y

y = 15

(c)

0

1

2

3

4

5

6

-30 -20 -10 0 10 20 30x (cm)

n (

10

11 c

m-3

)

Sum

Row1

Row2

Avg: all y

y = 22.5

(d)

Half-way between rows 1/4-way between rows

Directly under a row Beyond both rows

A tube spacing of 7” is chosen

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0

2

4

6

8

10

12

15 20 25 30L (cm)

Rip

ple

(+

/- %

)

L = 17.5 cm gives < 2% ripple at 17 cm below source

For a single row, a distance L = 17.5 cm between two tubes gives less than 2% ripple in density.


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An 8-tube linear test array

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165 cm

53.3 cm

17.8

17.8

17.8

17.8 cm73.7 cm

8.9 cm

x

y

Top view

Possible applications

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• Web coaters• Flat panel displays• Solar cells• Optical coatings

A web coater

The array source is vertically compact

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The magnets can be made in two pieces so that they hold each other on an aluminum sheet.

Once placed, the magnets cannot easily be moved, so for testing we use a wooden support.

165 cm

30 cm

15 cm

Side view

Probe ports

The wooden magnet frame is used in testing

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64"

21"

3.5"

12"

Wooden magnet support

2.00

5.00

3.75

2.5

24 ea. 2.5 x 5.5 x 1/2"4 ea. 2.5 x 64 x ¾”

1 ea. 21 x 64 x 1/2”16 ea. 1/4” diam dowels

Water and RF connections

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These will be shown in detail later

An 8-tube staggered array in operation

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Antennas

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The antennas are m = 0 loops made of three turns of 1/8” diam copper tubing.

The reason for m = 0 is that m = 1 antennas are too long, and much of the plasma is lost by radial diffusion before exiting the tube. The antenna must be close to the exit aperture and be tightly wound onto the tube.

The helicon wave pattern for m = 0 is a peculiar one but theory is straightforward. The wave changes from pure electromagnetic to pure electrostatic in each half cycle.

The RF system

UCLA

The critical elements are the junction box and the transmission lines.

Antenna connections (1)

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The antennas must be connected in parallel with cables of equal length.

The first trial was to use standard RG/8U cables and N connectors.

These arced and overheated.

Reason that RF connectors don’t work

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0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300 350 400Watts

Vol

ts p

-p

V p-p

Fit

0

2

4

6

8

10

12

14

0 50 100 150 200 250 300 350 400Watts

Am

ps r

ms

I rms

Fit

High voltages and currents occur when there is NO PLASMA; that is, before breakdown or when the plasma disrupts. Then, if the RF power on a tube is set for 400W, the peak-to-peak voltage can be 5kV, and the rms current can be 12A. Once the discharge is on, the RF power goes into the plasma rather than into the cables and connectors.

Antenna connections (2)

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In the second try, all connections were solidly soldered, and RG/393 teflon-insulated cable was used. This method works for CW operation in experiment

but may be marginal for industrial use.

Connections (3): a rectangular transmission line

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.25

0.70

ground

ground

HV RF

water in

water out

water at HV

1 1 10

000

cosh ( / ) cosh ( / ) 377 cosh ( / )

44 4r r r

h d h d h dZ

c

0 30ln(2 / )Z h d

For w >> h, we find

Impedance for various pipe diameters

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0

20

40

60

80

100

120

140

0 1 2 3 4 5 6h (in.)

Z0 (W

)0.25

0.375

0.5

0.625

0.75

0.875

1.0050W

d (in.)

For Z0 = 50W, h ~ 3/4”, but exactly 50W is not necessary

Transmission line construction (1)

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10.50

3.50

4.00

24.50

3.50

14.00

17.50

1.50

60.00


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0.25

1.25

Transmission line (4): water connections

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TOP SHEET

BOTTOM SHEET

14.00 14.0022.00

14.00 14.0022.00

7.007.00 7.007.507.507.007.007.00

28.50

1.50

1.50

8.50

8.50

No high voltage is applied along a water line.

Pictures (1)

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Pictures (2)

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Pictures (3)

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Design of the matching circuitUCLA

T 2 R2 X 2 B2 R(T 2 R)

C1 R

BC2

1

T 2(X B)

Z ZL cos(kz) j sin(kz)

cos(kz) jZL sin(kz)

“Standard” circuit “Alternate” circuit

Analytic formulas from Chen. The important part is that the impedance changes with cable length.

F.F. Chen, Capacitor tuning circuits for inductive loads, UCLA Rept. PPG-1401 (unpublished) (1992); F.F. Chen, Helicon Plasma Sources, in "High Density Plasma Sources", ed. by Oleg A. Popov (Noyes Publications, Park Ridge, NJ), Chap. 1 (1995)

Adapted to N tubes in parallel

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R, L

R, L

R, L

R, L

PS

N loads

Z2 - short cables

Distributor

Z1Z2

Z1 - long cable

C1C2

Matching ckt. 50W

The problem with array sources is that the cable lengths cannot be short. The match circuit cannot be close to all the tubes.

C1, C2 for N=8, L = 0.8H, Z1 = 110 cm, Z2 = 90 cm

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0

200

400

600

800

1000

1200

0 50 100 150 200Z1 (cm)

C (

pF)

C1(S)

C2(S)

0

200

400

600

800

1000

1200

1400

1600

0 50 100 150 200Z2 (cm)

C (

pF)

C1(S)

C2(S)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5R (ohms)

C (

pF)

C1(S)

C2(S)

0

200

400

600

800

1000

1200

1400

1600

0 0.5 1 1.5 2 2.5 3L (uH)

C (

pF)

C1(S)

C2(S)

Variation with the number of tubes N

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0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.5 1 1.5 2 2.5L (uH)

C1

(pF

)

8

6

4

2

1

N

0

100

200

300

400

500

600

700

800

0 0.2 0.4 0.6 0.8 1 1.2 1.4

L (uH)

C2

(pF

)

8

6

4

2

1

N

Note that it is not possible to match to 1 or 2 tubes with the same length cables used for 8 tubes.


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Experimental layout

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Staggered configuration

Compact configuration

Four probe positions

Effect of B-field strength (magnet height D)

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0

5

10

15

20

4 5 6 7 8 9 10 11

D (in)

n (

10

11 c

m-3

)

3kW2kW

Staggered, 20mTorrZ1 level, x=0", y=3.5"

0

1

2

3

4

4 5 6 7 8 9 10 11

D (in)

R(W

)

2kW3kW

Staggered, 20mTorr

Variation of density with D

Variation of loading resistance with D

Variation with RF power and Ar pressure

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0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200 220

P (mTorr)

n (1

01

1 c

m-3

)

3kW2kW

StaggeredZ1 level, x=0", y=3.5", D=7"

0

5

10

15

20

25

1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2

PRF (kW)

n (

10

11 c

m-3

)

Z1 levelZ2 level

Staggered, 20mTorr x=0", y=3.5", D=7"

Variation of density with RF power

Variation of density argon pressure

Density jump inside the tube

UCLA

0.01

0.1

1

10

100

0 50 100 150 200 250 300 350 400

Power per tube (W)

n (

10

11 c

m-3

)

0.10

0.50

1.00

Meas.

Rc (W)

compared with theory for various circuit resistances Rc

Deployment of movable probe array

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An linear array of 15 probes

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0.375Ó

19.75Ó

4.0"0.25Ó

H. Torreblanca, Multitube helicon source with permanent magnets, Thesis, UCLA (2008).

Density profiles across the chamber (1)

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0

4

8

12

16

20

-8 -6 -4 -2 0 2 4 6 8y (in)

n (1

011 c

m-3

)

Z1, x = 0Z1, x = 3.5Z2, x = 0Z2, x = 3.5

.

Staggered3kW, D=7", 20mTorr 0 3.5

Staggered configuration, 3kW

Side Langmuir probe

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0

2

4

6

8

10

-8 -6 -4 -2 0 2 4 6 8y (in)

n (1

011 cm

-3)

Z1, x = 0Z1, x = 3.5Z2, x = 0Z2, x = 3.5

Compact 3kW, D=7", 20mTorr

0 3.5

Compact configuration, 3kW

Side Langmuir probe


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0

1

2

3

4

5

-8 -6 -4 -2 0 2 4 6 8y(in)

n (1

011 c

m-

- 70714

x (in)Staggered3kW, D=7", 20mTorr


0 7-7 14


Bottom probe array

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Bottom probe array

0

2

4

6

8

10

-8 -6 -4 -2 0 2 4 6 8

y(in)

n (1

011 c

m-

-70714

Compact3kW, D=10", 20mTorr

x (in)0 7-7 14

UCLA

0

1

2

3

4

5

-8 -6 -4 -2 0 2 4 6 8 10 12 14 16x(in)

n (

10

11 c

m-

-3.503.5

Staggered, 3kW, D=7", 20mTorr y (in)

Density profiles along the chamber (1)


Bottom probe array

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0

1

2

3

4

5

-8 -6 -4 -2 0 2 4 6 8 10 12 14 16x(in)

n (

10

11 c

m-

-3.503.5

Staggered, 3kW, D=7", 20mTorr y (in)

Density profiles along the chamber (2)


Bottom probe array

Calibration of the collector array

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0

1

2

3

4

5

6

7

8

9

10

-8 -6 -4 -2 0 2 4 6 8y (in)

n (1

011 cm

-3)

LP, x = 0LP, x = 3.5LP over Al, x = 0LP over Al, x = 3.5ICC, x=0ICC, x=3.5

Compact, 2kW D=10", 20mTorr

0

1

2

3

4

5

6

7

8

9

10

-8 -6 -4 -2 0 2 4 6 8y (in)

n (1

011 cm

-3)

LP, x = 0LP, x = 3.5LP over Al, x = 0LP over Al, x = 3.5ICC, x = 0ICC, x = 3.5

Compact, 3kW, D=10", 20mTorr

0

1

2

3

4

5

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

y(in)

LP/(

LP o

ver

Al)

x=0x=3.5

0

1

2

3

4

5

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

y(in)

LP/IC

C

x=0x=3.5


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A compact, 8-tube module

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28.00

7.00 7.00 14.00

TOP VIEW OF ONE MODULE END VIEW

5.50

Stacked modules for large-area coverage

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Match circuit fits on top of module

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Ferrites for better coupling

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The RF energy outside the antenna is wasted.

Perhaps it can be captured with a ferrite cover.

Untested ideas

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One-piece ceramic tube

Ferrite transformer coupling

Varying the magnet shapes and spacings

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Varying the ID and OD of PMs shows that B depends mainly on total volume of magnet.

This shows that not much uniformity is lost if the magnet spacing is zero

design of pm helicon arrays

Documents

calculated field

field lines

tube length

discharge tubedesign

designed tube

density profilethe peak

multitube arraydesign

endplatethe peak