Helicons: A Physics Dilemma Solved

Helicons: A Physics Dilemma SolvedHelicons: A Physics Dilemma Solved

Francis F. Chen, UCLAFrancis F. Chen, UCLA

Tsing Hsua University, Taiwan, March 2008Tsing Hsua University, Taiwan, March 2008

How helicons started: 1962

UCLA

3kW17 MHz 500G

How helicons started: 1970 - 85

1 kW, 1 kG, argonn = 1013 cm-310X higher than normal

UCLA

--

+ --

+

--

+ --

+

(a)

(b)

(c)

B

In helicon sources, an antenna launches wavesin a dc magnetic field

The RF field of these helical waves ionizes the gas.The ionization efficiency is much higher than in ICPs.

A large number of problems arose

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• Absorption mechanism and efficiency• Weak m = –1 mode and the Big Blue Mode• Downstream density peak, axial ion flow• Non-monotonic axial decay• Triangular radial profile• Mass-dependent density limit• Low-field density peak (~30G)

• Density jumps with increasing B0, Prf

• Half-wave antenna better than full-wave

• Endplate charging with small diameters• High ion temperatures• Parametric instabilities

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--

+ --

+

--

+ --

+

(a)

(b)

(c)

B

In Landau damping, electrons surf on the wave

The helicon’s phase velocity is close to that of an electron near the peak of the ionization cross section (~100eV)

The Landau damping hypothesis

Landau damping disproved

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heater 0- +12V

bias 0- -200V

vacuum feedthrough

filament

anode

collector

grid

BN spacers grounded housing

ceramic covered wires

A fast (RF) energy analyzer was built and calibrated

RF modulated electron gunfor calibration

2-electrode gridded analyzerwith RF response

D.D. Blackwell and F.F. Chen, Time-resolved measurements of the EEDF in a helicon plasma, Plasma Sources Sci. Technol. 10, 226 (2001)

Time-resolved EEDFs show no fast electronsabove a threshold of 10 -4

0

20

40

60

0 50 100 150 200time (nsec)

Ele

ctro

n cu

rrent

(mA

)

0.0

0.1

1.0

10.0

100.0

1000.0

-15 -5 5 15 25Volts

I c (m

A)

3.35 eV

3.00 eV

0

1

2

3

-180 -90 0 90 180Antenna phasing (degrees)

Rp (

)

no plasma

0.0

0.4

0.8

1.2

-150 -100 -50 0 50Volts

I (m

A) 5 cm

10 cm

20 cm

Evolution of beam-created plasma

Distancefrom gun

0

10

20

30

0 25 50 75 100t (nsec)

I (m

A)

I-V swept by oscillating Vs I-V at two RF phases

Loading resistance agrees with calculations w/o L.D.

Injecting a current causes a beam-plasma instability

The Trivelpiece-Gould mode absorption mechanism

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• Helicon waves are whistler waves confined to a cylinder.

• Their frequencies are << c, so that normally me 0 is OK.

• However, if me 0, the dispersion relation has another root.

• The new root is an electron cyclotron wave in a cylinder. It is called a Trivelpiece-Gould (TG) mode.

• The TG mode exists in a thin layer near the surface and is damped rapidly in space, since it is slow. The helicon wave has weak damping.

• This mechanism was suggested by Shamrai and Taranov of Kiev, Ukraine, in 1995.

Why are helicon dischargessuch efficient ionizers?

Trivelpiece-Gould mode

Helicon mode

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4

r (cm)

P(r

) (

/ cm

2 )

Parabolic Profile: R = 1.47 Ohms

Square Profile: R = 1.71 Ohms

The helicon wave couples to an edge

cyclotron mode, which is rapidly

absorbed.

The H and TG waves differ in k

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0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 (cm-1)

k (c

m-1

)

20

30

60

300

B(G) n = 4x1011 cm-3

TG

H

This axis is essentially k

k||

Detection of TG mode was difficult

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RF PROBES

MAGNET COILS

MATCHING CIRCUIT RF

AXIAL PROBESANTENNA & SHIELD

0

2

4

6

8

10

12

14

-6 -4 -2 0 2 4 6r (cm)

J z, B

z (a

rb. u

nits

)

Jz calc

Bz calc

35G, 4E11

A

1

A

2

j

+

-

V = n A

1

A

2

0

Ž t

j n

co p p er fo il

return loop

Current probe

Return loop

Faraday shield

0

2

4

6

8

10

12

-6 -4 -2 0 2 4 6r (cm)

J z, B

z (a

rb. u

nits

)

Jz data

Bz data

30G, 2E11

An RF current probe had to be developed


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• Effect of endplates and endplate charging• High ion temperatures• Parametric instabilities

Types of antennas

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B

Nagoya Type III

Boswell double saddle coil

RH and LH helical

3-turn m = 0

The m = +1 (RH) mode gives much higher density

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0

1

2

3

4

-40 -20 0 20 40 60 80 100 120z (cm)

n (1

013

cm

-3)

(+1,+1)

(+1,-1)

(-1,+1)

(-1,-1)

B = 0

Comparison of time with space rotation

L = 10 cm RH mode

LH mode

m = +1 mode much stronger than m = –1 D.D. Blackwell and F.F. Chen, 2D imaging of a helicon discharge,Plasma Sources Sci. Technol. 6, 569 (1997)

m = –1

m = +1

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Reason m = -1 mode is not easily excited

The m = -1 mode has a narrower wave pattern; hence, it couples weakly to the TG mode at the boundary.

m = +1 m = -1

The dense core (n = 1013-14 cm-3) is due to neutral depletion, allowing Te to increase

No Faraday shield With shield

The Big Blue Mode


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• Endplate charging with small diameters• High ion temperatures• Parametric instabilities

Machine used for basic studies

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B 1kG, Prf 2kW @ 13-27 MHz, 1-10 MTorr Ar

r ~ 5 cmL ~ 160 cm

Symmetric and asymmetric antennas

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The maximum density occurs DOWNSTREAM, while Te decays.

This is due to pressure balance: nKTe = constant.

Line radiation is main loss in Te decay

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Non-monotonic decay of wave downstream

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Oscillations are due to beating of radial modes with different k||. Theory fails as density changes further out.

Average decay rate agrees with collisional damping.

Triangular density profiles

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0.0

0.5

1.0

1.5

2.0

2.5

-5 -4 -3 -2 -1 0 1 2 3 4

r (cm)

n (

1013

cm-3

)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2r / a

n /

n o

heat source

Nonlinear diffusion, coupled with a bimodal ionization source, can explain "triangular" density profiles.


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• Endplate charging with small diameters

• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities

Mass-dependent density limit

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As B0 is increased, n rises but saturates at a value depending on the ion mass. This effect was first observed by T. Shoji.

A drift-type instability occurs

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L

H

2 0

0

f( K H z )

0 1.0 1.5B0

(KG)0.5

2 . 0

0

n e

( 1 0 1 3 / c m 3 )

M. Light (Ph.D. thesis) found that an instability occurs at a critical field and causes the density to saturate.

This is the oscillation spectrum for neon.

He identified the instability as a drift-Kelvin Helmholtz instability and worked out the theory for it.

M. Light, F.F. Chen, and P.L. Colestock, Plasma Phys. 8, 4675 (2001), Plasma Sources Sci. Technol. 11, 273 (2003)

Anomalous diffusion results

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-0.5

0

2

0 1600

(m-2s-1)

B0 (KG)

10 21

Calculated

Measured

Outward particle flux was measured with n – correlations, agreeing with that calculated quasilinearly from the growth rate.

Density limit due to neutral depletion

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Axial density profile with two 2-kW antennas 1m apart


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A density peak occurs at low B-fields

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The cause is the constructive interference of the reflected wave from a bidirectional antenna

HELIC computations of plasma resistance

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 50 100 150 200B (G)

R (

ohm

s)

2E+11

4E+11

6E+11

8E+11

1E+12

n (cm-3)

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

Vary the B-field Vary the endplate distance

Vary the with endplate conductivity Uni- and b-directional antennas

The end coils can also be turned off or reversed to form a cusped B-field

to pump

END COILS

The field lines then end on the glass tube, which forms an insulting endplate. An aperture limiter can also be added.

A cusp field or and end block can greatly increase the density

G. Chevalier and F.F. Chen, Experimental modeling of inductive discharges, J. Vac. Sci. Technol. A 11, 1165 (1993)


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Discharge jumps into helicon modes

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R.W. Boswell, Plasma Phys. Control. Fusion 26, 1147 (1984)

n vs. RF power n vs. B-field

Transition to helicon mode

UCLAA.W. Degeling and R.W. Boswell, Phys. Plasmas 4, 2748 (1997)

E: capacitive

H: inductive

W: helicon

A new interpretation of the jumpsUCLA

1

10

100

1000

0.01 0.1 1 10 100

n (1011 cm-3)

Pin

(W

per

tub

e)

400W, ICP

400

300

200

100

50

20

Loss

Prf (W)B = 80G

Rc = 0.5 pin rf

p c

RP P

R R

The power into the plasma depends on the plasma loading (Rp) and the circuit losses (Rc)

If Rp is too small, the input power is less than the losses.

The jump into helicon mode can be computed from theoretical Rp’s. The critical power agrees with experiment.

F.F. Chen and H. Torreblanca, Plasma Sources Sci. Technol. 16, 593 (2007)


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A 1-inch diam helicon discharge

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Critical field is where rLe ~ a

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Half wavelength helical antennas are betterthan full wavelength antennas

L. Porte, S.M. Yun, F.F. Chen, and D. Arnush, Superiority of half-wavelength helicon antennas, LTP-110 (Oct. 2001)

0

1

2

3

4

0 20 40 60 80z (cm)

n (1

01

3cm

-3)

10cm half wavelength

15cm full wavelength

20cm full wavelength


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Anomalously high ion temperatures

J.L. Kline, E.E. Scime, R.F. Boivin, A.M. Keesee, and X. Sun, Phys. Rev. Lett. 88, 195002 (2002).

Unusually high Ti’s are observed by laser induced fluorescence. This happens near lower hybrid resonance, but no special heating is expected there.


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The energy absorption mechanism near the antenna may be nonlinear, involving parametric decay of the TG wave into ion acoustic waves

Lorenz, Krämer, Selenin, and Aliev* used:

1. Test waves in a pre-formed plasma

2. An electrostatic probe array for ion oscillations

3. Capacitive probes for potential oscillations

4. Microwave backscatter on fluctuations

5. Correlation techniques to bring data out of noise

*B. Lorenz, M. Krämer, V.L. Selenin, and Yu.M. Aliev, Plasma Sources Sci.Technol. 14, 623 (2005).

A helicon wave at one instant of time

UCLANote that the scales are very different!

Damping rate in the helicon afterglow

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The damping rate increases with Prf, showing the

existence of a nonlinear damping mechanism.

Excitation of a low-frequency wave

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The LF wave is larger with the e.s. probe than with the capacitive probe, showing that the wave is electrostatic.

As Prf is raised, the sidebands

get larger due to the growth of the LF wave.

Oscillations are localized in radius and B-field

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The fluctuation power and the helicon damping rate both increase nonlinearly with rf power.

Proposed parametric matching conditions

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k1k2

k0

0 1 2

0 1 2

0 1 2 1 20,

k k k

k k k k k

k0 = helicon wave, k1 = ion acoustic wavek2 = Trivelpiece-Gould mode

This was verified experimentally.

Evidence for m = 1 ion acoustic wave

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The cross phase between two azimuthal probes reverses on opposite sides of the plasma.

k is larger than kr, and both

increase linearly with frequency.

From the slope one can calculate the ion acoustic velocity, which

yields Te = 2.8 eV, agreeing with 3 eV from probe measurements.

With a test pulse, the growth rate can be seen directly

From probe data From wave backscatter

Growth rate vs. power Growth rate vs. power

Conclusion on parametric instabilities

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Kramer et al. showed definitively that damping of helicon waves by parametric decay occurs near the axis. They identified the decay waves, checked the energy balance, and even checked the calculated instability threshold and growth rate.

However, this process is too small to be the major source of energy transfer from the antenna to the plasma. It is still unknown what happens under the antenna, where it is difficult to measure. It could be that the waves observed were actually created under the antenna but measured

downstream.

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Helicons: A Physics Dilemma Solved