helicons: a physics dilemma solved francis f. chen, ucla tsing hsua university, taiwan, march 2008
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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
UCLA
• 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
UCLA
--
+ --
+
--
+ --
+
(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
UCLA
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
UCLA
• 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
UCLA
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
UCLA
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
A large number of problems arose
UCLA
• 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
• Effect of endplates and endplate charging• High ion temperatures• Parametric instabilities
Types of antennas
UCLA
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
UCLA
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
UCLA
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
A large number of problems arose
UCLA
• 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
Machine used for basic studies
UCLA
B 1kG, Prf 2kW @ 13-27 MHz, 1-10 MTorr Ar
r ~ 5 cmL ~ 160 cm
Symmetric and asymmetric antennas
UCLA
The maximum density occurs DOWNSTREAM, while Te decays.
This is due to pressure balance: nKTe = constant.
Line radiation is main loss in Te decay
UCLA
Non-monotonic decay of wave downstream
UCLA
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
UCLA
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.
A large number of problems arose
UCLA
• 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
• Endplate charging with small diameters
• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities
Mass-dependent density limit
UCLA
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
UCLA
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
UCLA
-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
UCLA
Axial density profile with two 2-kW antennas 1m apart
A large number of problems arose
UCLA
• 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
• Endplate charging with small diameters
• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities
A density peak occurs at low B-fields
UCLA
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)
A large number of problems arose
UCLA
• 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
• Endplate charging with small diameters
• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities
Discharge jumps into helicon modes
UCLA
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)
A large number of problems arose
UCLA
• 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
• Endplate charging with small diameters
• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities
A 1-inch diam helicon discharge
UCLA
Critical field is where rLe ~ a
UCLA
A large number of problems arose
UCLA
• 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
• Endplate charging with small diameters
• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities
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
A large number of problems arose
UCLA
• 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
• Endplate charging with small diameters
• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities
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.
A large number of problems arose
UCLA
• 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
• Endplate charging with small diameters
• Half-wave antenna better than full-wave• High ion temperatures• Parametric instabilities
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
UCLA
The damping rate increases with Prf, showing the
existence of a nonlinear damping mechanism.
Excitation of a low-frequency wave
UCLA
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
UCLA
The fluctuation power and the helicon damping rate both increase nonlinearly with rf power.
Proposed parametric matching conditions
UCLA
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
UCLA
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
UCLA
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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