How helicons started: 1962 UCLA 3kW 17 MHz 500G

How helicons started: kW, 1 kG, argon n = 1013 cm-3 10X higher than normal

UCLA In helicon sources, an antenna launches waves in 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 B 0, P rf Half-wave antenna better than full-wave Endplate charging with small diameters High ion temperatures Parametric instabilities

UCLA 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 A fast (RF) energy analyzer was built and calibrated RF modulated electron gun for calibration 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)

Time-resolved EEDFs show no fast electrons above a threshold of I-V swept by oscillating V s 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 m e  0 is OK. However, if m e  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 discharges such efficient ionizers? The helicon wave couples to an edge cyclotron mode, which is rapidly absorbed.

The H and TG waves differ in k  UCLA This axis is essentially k  k ||

Detection of TG mode was difficult UCLA 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 B 0, P rf Half-wave antenna better than full-wave Effect of endplates and endplate charging High ion temperatures Parametric instabilities

Types of antennas UCLA 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 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 = +1m = -1

The dense core (n = 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 B 0, P rf 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, P rf  MHz, 1-10 MTorr Ar r ~ 5 cm L ~ 160 cm

Symmetric and asymmetric antennas UCLA The maximum density occurs DOWNSTREAM, while Te decays. This is due to pressure balance: nKT e = constant.

Line radiation is main loss in T e 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 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 B 0, P rf Endplate charging with small diameters Half-wave antenna better than full-wave High ion temperatures Parametric instabilities

Mass-dependent density limit UCLA As B 0 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 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 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 B 0, P rf 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 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 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 B 0, P rf 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 UCLA A.W. Degeling and R.W. Boswell, Phys. Plasmas 4, 2748 (1997) E: capacitive H: inductive W: helicon

A new interpretation of the jumps UCLA The power into the plasma depends on the plasma loading (R p ) and the circuit losses (R c ) If R p is too small, the input power is less than the losses. The jump into helicon mode can be computed from theoretical R p ’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 B 0, P rf 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 r Le ~ 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 B 0, P rf Endplate charging with small diameters Half-wave antenna better than full-wave High ion temperatures Parametric instabilities

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

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 B 0, P rf 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, (2002). Unusually high T i ’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 B 0, P rf 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 UCLA Note that the scales are very different!

Damping rate in the helicon afterglow UCLA The damping rate increases with P rf, 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 P rf 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 k1k1 k2k2 k0k0 k 0 = helicon wave, k 1 = ion acoustic wave k 2 = 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 k r, and both increase linearly with frequency. From the slope one can calculate the ion acoustic velocity, which yields T e = 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

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.

Many problems have been solved, but some still remain! 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 B 0, P rf Endplate charging with small diameters Half-wave antenna better than full-wave High ion temperatures Parametric instabilities Current project: Commercialization of an industrially viable helicon source using permanent magnets for the dc field, and multiple sources for large-area coverage.

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