Transcript Slide 1

Helicons: A Physics Dilemma Solved
Francis F. Chen, UCLA
Tsing Hsua University, Taiwan, March 2008
How helicons started: 1962
3kW
17 MHz
500G
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How helicons started: 1970 - 85
1 kW, 1 kG, argon
n = 1013 cm-3
10X higher than normal
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B
(a)
In helicon
sources,
an antenna launches waves
-+
in a dc magnetic field
--
+
--
+
+
--
(b)
(c)
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
• 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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The Landau damping hypothesis
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)
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Landau damping disproved
A fast (RF) energy analyzer was built and calibrated
vacuum feedt hrough
col lect or
fi lament
heater
-0- +12V
anode
ceramic cov ered wires
g rid
bias
-0- -200V
BN s pacers
RF modulated electron gun
for calibration
g ro un d ed h o us in g
2-electrode gridded analyzer
with 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)
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Time-resolved EEDFs show no fast electrons
above a threshold of 10 -4
60
1 0 0 0 .0
3 .3 5 e V
40
1 0 .0
Ic (mA)
Electron current (mA)
1 0 0 .0
1 .0
20
0 .1
3.00 eV
0
0 .0
0
50
100
150
200
- 15
time (nsec)
-5
I-V swept by oscillating Vs
5
Vo lt s
15
25
I-V at two RF phases
3
1.2
Evolution of beam-created plasma
30
20
0.8
D is tanc e
I (mA)
2
fro m gu n
I (mA)
R p ( )
10
1
5 cm
10 cm
0
0
25
50
t (nsec)
75
100
20 cm
0.4
n o p la s m a
0.0
0
-180
-90
0
90
A n te n n a p h a s in g (d e g r e e s )
Loading resistance agrees with
calculations w/o L.D.
180
-150
-100
-50
Volts
0
50
Injecting a current causes a
beam-plasma instability
The Trivelpiece-Gould mode absorption
mechanism
• 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.
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Why are helicon discharges
such efficient ionizers?
Trivelpiece-Gould mode
The helicon wave
couples to an edge
cyclotron mode,
which is rapidly
absorbed.
Helicon mode
2
P(r) (  / cm )
1.2
1.0
Parabolic Profile: R = 1.47 Ohms
0.8
Square Profile: R = 1.71 Ohms
0.6
0.4
0.2
0.0
0
1
2
r (cm)
3
4
The H and TG waves differ in k
1.0
n = 4x1011 cm-3
B(G)
20
30
60
300
-1
k (cm )
0.8
k||
0.6
TG
0.4
H
0.2
0.0
0
1
2 -1
b (cm )
3
4
This axis is essentially k
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Detection of TG mode was difficult
14
RF PROBES
35G, 4E11
MAGNET COILS
ANTENNA & SHIELD
AXIAL PROBES
Jz, Bz (arb. units)
12
10
8
6
Jz calc
Bz calc
4
2
MATCHING CIRCUIT
RF
0
-6
Faraday shield
-4
-2
0
r (cm)
2
4
6
12
30G, 2E11
Jz, Bz (arb. units)
10
8
6
Jz data
Bz data
4
2
Return loop
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0
-6
-4
-2
0
r (cm)
2
4
6
An RF current probe had to be developed
A large number of problems arose
• 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
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Types of antennas
B
RH and LH helical
Nagoya Type III
Boswell double saddle coil
3-turn m = 0
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The m = +1 (RH) mode gives much higher density
Comparison of time with space rotation
4
L = 10 cm
(+1,+1)
(+1,-1)
(-1,+1)
(-1,-1)
B=0
RH mode
n (10
13
-3
cm )
3
2
1
LH mode
0
-40
-20
0
20
40
z (cm)
60
80
100
120
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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
m = +1
m = -1
The m = -1 mode has a narrower wave pattern; hence, it
couples weakly to the TG mode at the boundary.
The Big Blue Mode
The dense core (n = 1013-14 cm-3) is due to neutral
depletion, allowing Te to increase
No Faraday shield
With shield
A large number of problems arose
• 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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Machine used for basic studies
r ~ 5 cm
L ~ 160 cm
B  1kG, Prf  2kW @ 13-27 MHz, 1-10 MTorr Ar
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Symmetric and asymmetric antennas
The maximum density occurs DOWNSTREAM, while Te decays.
This is due to pressure balance: nKTe = constant.
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Line radiation is main loss in Te decay
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Non-monotonic decay of wave downstream
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.
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Triangular density profiles
1.0
2.0
0.8
1.5
0.6
n / no
n (1013cm-3 )
2.5
1.0
0.4
0.5
0.2
0.0
heat source
0.0
-5
-4
-3
-2
-1
0
r (cm)
1
2
3
4
0.0
0.2
0.4
0.6
r/a
0.8
1.0
Nonlinear diffusion, coupled with a bimodal ionization
source, can explain "triangular" density profiles.
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1.2
A large number of problems arose
• 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
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Mass-dependent density limit
As B0 is increased, n rises but saturates at a value depending
on the ion mass. This effect was first observed by T. Shoji.
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A drift-type instability occurs
H
20
L
f
(KHz)
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.
0
2.0
ne
(1013/cm3)
M. Light, F.F. Chen, and P.L. Colestock,
Plasma Phys. 8, 4675 (2001), Plasma
Sources Sci. Technol. 11, 273 (2003)
0
0
0.5 B (KG) 1.0
1.5
0
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Anomalous diffusion results
2

Calculated
-2 -1
(m s )
10
21
Measured
0
-0.5
0
B (KG)
0
1600
Outward particle flux was measured with n – f correlations,
agreeing with that calculated quasilinearly from the growth rate.
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Density limit due to neutral depletion
Axial density profile with two 2-kW antennas 1m apart
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A large number of problems arose
• 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
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A density peak occurs at low B-fields
The cause is the constructive interference of the
reflected wave from a bidirectional antenna
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HELIC computations of plasma resistance
3.0
d
2E+11
4E+11
6E+11
8E+11
1E+12
2.0
5 cm
10 cm
No bdy
5
4
R (ohms)
2.5
R (ohms)
6
n (cm-3)
1.5
3
1.0
2
0.5
1
0
0.0
0
50
100
150
200
B (G)
Vary the B-field
Vary the with endplate conductivity
0
50
100
150
200
250
300
B (G)
Vary the endplate distance
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
• 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
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Discharge jumps into helicon modes
n vs. RF power
n vs. B-field
R.W. Boswell, Plasma Phys. Control. Fusion 26, 1147 (1984)
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Transition to helicon mode
W: helicon
H: inductive
E: capacitive
A.W. Degeling and R.W. Boswell, Phys. Plasmas 4, 2748 (1997)
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A new interpretation of the jumps
1000
P in (W per tube)
Prf (W)
100
B = 80G
Rc = 0.5
400W, ICP
400
300
200
100
50
20
Loss
Pin  Prf
R p  Rc
The power into the plasma
depends on the plasma loading
(Rp) and the circuit losses (Rc)
10
1
0.01
Rp
0.1
1
n (1011 cm-3)
10
100
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
• 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
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A 1-inch diam helicon discharge
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Critical field is where rLe ~ a
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A large number of problems arose
• 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
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Half wavelength helical antennas are better
than full wavelength antennas
4
13
-3
n (10 cm )
3
2
10cm half wavelength
15cm full wavelength
20cm full wavelength
1
0
0
20
z (cm)
40
60
L. Porte, S.M. Yun, F.F. Chen, and D. Arnush, Superiority of half-wavelength helicon antennas, LTP-110 (Oct. 2001)
80
A large number of problems arose
• 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
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Anomalously high ion temperatures
Unusually high Ti’s are observed by
laser induced fluorescence.
This
happens near lower hybrid resonance,
but no special heating is expected
there.
J.L. Kline, E.E. Scime, R.F. Boivin, A.M. Keesee, and X. Sun, Phys. Rev. Lett. 88, 195002 (2002).
A large number of problems arose
• 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
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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
Note that the scales are very different!
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Damping rate in the helicon afterglow
The damping rate increases with Prf, showing the
existence of a nonlinear damping mechanism.
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Excitation of a low-frequency wave
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.
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Oscillations are localized in radius and B-field
The fluctuation power and the
helicon damping rate both
increase nonlinearly with rf
power.
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Proposed parametric matching conditions
k2
k1
0  1  2
k 0  k1  k 2
k0
k 0  k 1  k 2  0, k 1  k 2
k0 = helicon wave, k1 = ion acoustic wave
k2 = Trivelpiece-Gould mode
This was verified experimentally.
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Evidence for m = 1 ion acoustic wave
The cross phase between two
azimuthal probes reverses on
opposite sides of the plasma.
kq 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.
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With a test pulse, the growth rate can be seen directly
From probe data
Growth rate vs. power
From mwave backscatter
Growth rate vs. power
Conclusion on parametric instabilities
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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Title here