Helicon mode formation and rf power deposition in a helicon source

Transcription

1 Helicon mode formation and rf power deposition in a helicon source Michael Krämer & Kari Niemi Institut für Experimentalphysik II, Ruhr-Universität D-4478 Bochum, Germany Helicon Mini-Conference APS-DPP, Orlando, FL Outline Introduction: rf absorption & electron heating in helicon plasmas Basics of the helicon discharges, Helicon experiment Helicon mode formation: field distribution, dispersion rf power deposition: linear and/or nonlinear absorption, effect of electrostatic fluctuations Summary Electron helicon wave resonance (ω /k = v the ): Landau damping (linear), velocity diffusion (quasilinear), trapping (nonlinear) electron heating; observations at lower magnetic field and lower density Mode conversion (linear): Coupling of helicon and Trivelpiece-Gould waves; generally close to plasma edge. Parametric instabilities (nonlinear): RF power transfer from helicon wave into strongly damped electrostatic fluctuations Lorenz, Krämer, Selenin & Aliev, PSST 14, 63 (5).

2 Helicon Experiment HE-L RF power coupling: Exp. parameters: f RF = MHz, f pulse = 5 or 5 Hz, t pulse = - 8 ms, P RF 1.5 kw, m = 1 helical antenna n e x1 19 m -3, T e 3 ev, T i <. ev, B = 1-1 mt, p =.1-1 Pa argon (flow 7 sccm), quartz tube, r tube = 73 mm, l tube = 11 mm Krämer, Lorenz & Clarenbach, PSST 11A, 1 ()

3 Basics helicon modes excited via helical antenna The RF power is inductively coupled to the helicon discharge by antennas exciting helicon modes with different azimuthal mode numbers. The fields of a particular mode vary as exp[ im ( ϑ + kz z ω t)]. Helical antennas excite predominantly m = +1 helicon modes on one side of the antenna, m = -1 modes on the other side. E.M. fields: Rotational and potential electric fields mainly perpendicular to B. Three components of magnetic field. rf currents follow rf magnetic field. + B m = -1, -k z m = +1, +k z Helical currents couple to RF magnetic fields (solid lines) of the helicon mode; RF electric fields as dashed lines.

4 Basics rf power deposition for helical antenna absorbed power density (a.u.) j E j z E z n e = 1 19 m -3, w p = 4 mm B = 4 mt f = MHz m = +1 j E Radial absorbed power density profiles from helicon wave guide model (EMHD) P ( Wm -1 ) B = 45 mt p=.5 Pa n e = 1*1 19 m -3 w p ( mm ) z ( m ) m = +1 flat profile narrow profile Abs. power per length from antenna- plasma model (fully e.m.) Krämer at al., PSST 11A, 1 () m = -1 RF power absorption from perpendicular ( ) and parallel (z) electron currents and electric fields; maximum absorption on axis Peaked density profiles Increasing axial asymmetry of RF power deposition with narrowing of radial density profiles due to suppression of m = -1 modes Energy flux associated with helicon mode propagation mainly in positive (m = +1 mode) magnetic field direction Axial asymmetry of helicon discharge

5 Basics 7.3 maximum heating on axis (arb. u.) intensity, I s I ArII I S m = +1 (arb. u.) intensity, I s I ArII I S m = r (m ) r (m ) T e (ev).8 B = 55 mt p Ar =.3 Pa P 1 W.6 z = 49 cm.4.. T e (ev) n e (a.u.) model r (cm) n e (a.u.) On m = +1 side, pronounced peak of 48.6 nm Ar ion line (blue core ) on axis significant electron heating. Clarenbach, Krämer & Lorenz, J.Phys.D:Appl.Phys. 4 (7) 5117 Consistent with T e peak at r =. Density profile in accordance with simple diffusion model with line source on axis.

6 Basics Evolution of the helicon discharge (1) Movie of Langmuir (n e I sat ) & rf (Bdot: B r ) probe measurements Transition: CCP ICP Helicon-produced plasma Helicon waves start propagating with long axial wavelength according to helicon dispersion relation Maximum absorption on axis ω ω kk k k n pe z z λ 1/ z e c ωce peaked density profile Axial energy flux associated with helicon mode propagation mainly in positive (m = +1 mode) magnetic field direction Axial asymmetry of helicon discharge

7 Evolution of helicon discharge ().5.5: B = 54 mt, p ar =.6 Pa, main rf pulse = 1.5 ms B r from B-dot probe, n e from Langmuir probe, rf energy density = B r ( ) + B r (9 ) B r - (a. u.) B r - 9 (a. u.) energy (a. u.) t=,1 ms I sat (a. u.) Ion sat. current: I min = I max =.48 ΔI = 4.9e-3 Note: Scaling changes in subsequent plots

8 Evolution of helicon discharge () B r from B-dot probe, n e from Langmuir probe, rf energy density = B r ( ) + B r (9 ) B r - (a. u.) B r - 9 (a. u.) energy (a. u.) t=,3 ms I sat (a. u.) Ion sat. current: I min = I max =.4 ΔΙ = 5.79e

9 Evolution of helicon discharge () B r from B-dot probe, n e from Langmuir probe, rf energy density = B r ( ) + B r (9 ) B r - (a. u.) B r - 9 (a. u.) energy (a. u.) t=,4 ms I sat (a. u.) Ion sat. current: I min = -.4 I max =.59 ΔΙ = 9.9e

10 Evolution of helicon discharge () B r from B-dot probe, n e from Langmuir probe, rf energy density = B r ( ) + B r (9 ) B r - (a. u.) B r - 9 (a. u.) energy (a. u.) t=,46 ms I sat (a. u.) Ion sat. current: I min = -.4 I max =.84 ΔΙ = 1.4e

11 Evolution of helicon discharge () B r from B-dot probe, n e from Langmuir probe, rf energy density = B r ( ) + B r (9 ) B r - (a. u.) B r - 9 (a. u.) energy (a. u.) t= 1 ms I sat (a. u.) Ion sat. current: I min = I max =.15 ΔΙ = 1.5e

12 Helicon mode formation D helicon wave field Amplitude (left) and phase (right) of the magnetic field components in the quasi-stationary helicon discharge during the main rf pulse; B = 5 mt, p Ar =.6 Pa, P = 1.5 kw Oblique wave propagation from the antenna to the center Well-defined axial wavelength s (cm) s (cm) s (cm) a) 6 B r (mt) B θ (mt) B z (mt) z (cm) s (cm) s (cm) s (cm) b) ϕ r ( ) ϕ θ ( ) ϕ z ( ) z (cm) amplitude phase

13 Helicon mode formation plasma density and magnetic energy Radial profiles of the electron density, the magnetic field amplitudes and the rf energy density for high and low rf power. n e (1 19 m -3 ) n e (1 19 m -3 ) Measuring position 4 cm away from center of antenna, B = 5 mt, p Ar =.6 Pa, P = 1.5 kw / 1 W B comp. (mt)..1 B r B θ B z k z = 3.5 m -1 B comp. (mt).1.5 B r B θ B z k z = 9.1 m -1 rf magnetic energy profiles are much narrower for high rf power than for low power. Asymmetry correlated with off-axis peak on density profile a) r (cm) B ((mt) ) k z = 3.5 m b) r (cm) B ((mt) ) high rf power low rf power k z = 9.1 m -1

14 Helicon mode formation profiles of plasma density & magn. energy (EMHD model) n e (1 19 m -3 ) n e (1 19 m -3 ) Radial profiles of electron density (top), magnetic field amplitudes (middle, top), rf energy density (middle, bottom) absorbed power density (bottom) B = 5 mt, p Ar =.6 Pa, P = 1.5 kw / 1 W rf magnetic energy profiles are much narrower for high rf power than for low power. Steep density gradient near center at high power causes rf absorption peak off axis. Q (1 5 W/m 3 ) B ((mt) ) B comp. (mt) a) for P z,tot = 4 W. k z = 48.1 m -1 B r.1 B θ B z for P z,tot = 4 W.1 k z = 48.1 m -1.5 for T 1.5 e = 3 ev, P z,tot = 4 W, k 1. z = 48.1 m r (cm) Q (1 5 W/m 3 ) B comp. (mt) B ((mt) ) for P z,tot = 1 W.1 k z = 47.8 m -1 B r.5 B θ B z for P z,tot = 1 W k z = 47.8 m -1.1 for T.15 e = ev, P z,tot = 1 W, k.1 z = 47.8 m r (cm) high rf power low rf power b)

15 Helicon mode formation rf energy profiles & helicon dispersion Quantitative comparison with theoretical predictions taking the measured axial wavenumber: 1. Modeling (EMHD) of the magnetic field and energy profiles assuming a uniform plasma column (simple dispersion relation) k 134 m -1.. Estimate radial wavenumber from the width of n e (r) effective plasma radius a and from B r (a) = k 1 m -1. In both cases, the resulting B profiles significantly are wider than measured; even for low rf power, calculated profiles wider by factor 1.6 (1.) and 1.9 (.), respectively.

16 RF power deposition axial energy flux s (cm) 5-5 S z (1 5 W/m ) s (cm) 5-5 S z (1 5 W/m ) a) z (cm) high rf power b) z (cm) low rf power Axial Poynting B = 5 mt, p Ar =.6 Pa, P = 1.5 kw / 1 W The axial energy flux is more strongly focussed for high power than for low power. (a) P rf, h = 1.5 kw: P abs, h = 313W (1 %), (b) P rf, l = 1 W: P abs, l = 4 W (4 %).

17 RF power deposition abs. power from meas. field & linear model s (cm) 5-5 Q (1 5 W/m 3 ) s (cm) 5-5 Q (1 5 W/m 3 ) z (cm) z (cm) (a) high rf power (b) low rf power Absorbed power B = 5 mt, p Ar =.6 Pa; (a) P = 1.5 kw, k z = 3.5 m -1, T e = 3 ev; (b) P = 1 W, k z = 9.1 m -1, T e = ev Absorbed power from linear EMHD model much lower than measured power: (a) P rf, h = 1.5 kw: P ca, h = 4.1W P abs, h = 313W = 7.8 x P ca,h (b) P rf, l = 1 W: P ca, l = 11.7 W P abs, l = 4. W = 3.4 x P ca,l

18 RF power deposition 4 variation of rf power 1, P (kw), T e (ev) 3 1 n e l (m - ) T e (ev) P (kw),8,6,4, n e l (1 18 m - ) t (μs) Evolution of electron temperature and density (line-integrated)

19 RF power deposition helicon wave damping (a) r (cm) z (cm) p AR =.3 Pa B = 55 mt P RF1 = 96 W -1 1 B-dot probe signal (norm.) (b) avg. wave energy (a.u.) antenna p AR =.3 Pa B = 55 mt P RF1 = 96 W z (cm) Axial damping decrement k zi = Im(k z ) from decrease of RF energy integrated over cross section

20 RF power deposition excitation of density fluctuations r (cm) B = 55 mt, p Ar =.3 Pa, P rf 1 W z (cm) B r (mt) r (cm) 6 B = 55 mt, p Ar =.3 Pa, P rf 1 W z (cm) δn.5 (a.u.) rf magnetic field energy density fluctuation amplitude (lf) Helicon wave excites electrostatic fluctuations; fluctuation level high, where field energy is high

21 RF power deposition variation of rf power (continued) k zi (m -1 ) P (W) k zi (m -1 ) measurement k zi (m -1 ) model n e fluct. degree (%) P (dbm).6.4. n e fluctuation degree (%) Damping decrement k zi & density fluctuation level (f =.3-5 MHz) vs. rf power. Measuring position 4 cm from center of antenna.- B = 5 mt, p Ar =.6 Pa. At small rf power, damping 3x stronger than predicted from linear theory Damping along with the fluctuation level increases with the rf power. Threshold behavior suggests that the rf power is dissipated via parametrically excited electrostatic fluctuations.

22 Summary Strong focussing of helicon wave energy, particularly at high rf power due to peaked density profiles. However, from comparison with computations (helicon waveguide model) helicon mode dispersion cannot be explained. rf power deposited in helicon discharge determined in absolute units; for P rf = 1.5 kw, rf power deposited 3 W or %, for P rf = 1 W, rf power deposited 4 W or 4 %. Nevertheless, rf power is much higher than predicted: Absorbed power from linear EMHD model accounting for collisional and Landau damping is much lower than measured power, i.e., by factors 3.4/ 7.8 for low/ high powers. The above results are consistent with measurements of helicon damping: - for low power, damping is 3 times higher than predicted; - above threshold power, damping increases with rf power; - simultaneous onset of electrostatic fluctuations mainly excited in the center, where the rf energy has a maximum, suggests dissipation via parametrically excited electrostatic fluctuations.