Two ion species studies in LAPD * Ion-ion Hybrid Alfvén Wave Resonator

Transcription

1 Two ion species studies in LAPD * Ion-ion Hybrid Alfvén Wave Resonator G. J. Morales, S. T. Vincena, J. E. Maggs and W. A. Farmer UCLA Experiments performed at the Basic Plasma Science Facility (BaPSF) Sponsored by: ONR-MURI *S. T. Vincena, G. J. Morales and J. E. Maggs, Physics of Plasmas 17, (2010)

2 Motivation Shear Alfvén waves in two-ion species plasmas (a.k.a. ion cyclotron waves, EMIC, ion-hybrid waves etc..) interact strongly with ions Altitude-sensitive noise detected by spacecraft in H + -He + geoplasma 5. M. Temerin and R.L. Lysak, J. Geophys. Res. 89, 2849 (1984). Ion acceleration in solar corona 6. K. G. McClements and L. Fletcher, Astrophys. J. 693, 1494 (2009). Possible wave resonators in equatorial region of planetary magnetospheres----resonance MISSION 7. A.V. Gigliemi, A.S. Potapov, and C.T. Russell, Pis ma v ZhETF 72, 432 (2000). 8. A. G. Demekhov, V. Y. Trakhtengerts, M. M. Mogilevsky, and L. M. Zelenyi Adv. Space Res. 32, 355 (2003). 2

3 Essential Physics--I For small transverse scales the compressional mode is evanescent Shear Alfvén wave dispersion relation is well approximated by k 2 II = ω 2 ε c 1 k c 2 1 ω ε II k B 0 For two cold ion species ε 2 ω p1 Ω 2 1 ω + ω p 2 2 Ω 2 2 ω 2 2 Perpendicular dielectric vanishes at ω ii = ω 2 p1ω ω 2 2 p 2 Ω 1 ω 2 2 p1 + ω p 2 and singular at ω = Ω 1 and ω = Ω 2 3

4 Essential Physics--II Frequency ω and k are set by source Axial cut-off occurs when ε = 0 For cold ions at ω = ω 2 p1ω ω 2 2 p2 Ω 1 Ω ω 2 2 ii p1 + ω p2 But when k ρ i is not negligible ( ) ε = 1 + ω 2 2 pe ω ps e ( k ρ s ) 2 I l k 2 2 ρ Ω e 2 s k ρ s ω 2 ( lω s ) 2 s l =1 Vanishes at frequencies corresponding to pure IBW Consequence: shear Alfvén wave experiences multiple propagation bands between the lower and the higher cyclotron frequencies that become more pronounced at large ion temperatures or small transverse scales

5 Effect of Species (He/Ne) Concentration for Cold Ions Contour in frequency-radial position space at fixed axial location z = 4 m B θ (ω,r) 100% He 50%He-50%Ne 20%He-80%Ne Wave frequency scaled to Neon cyclotron frequency ω Ω Ne Ω He Ω ii Propagation gap Ω Ne 8 cm Radial position across magnetic field Typical LAPD parameters N e =10 12 cm -3 ; B 0 = 750G ; T e = 5 ev; T i = 0; a = 1 cm

6 Modification of Cold Propagation Gap by Ion Temperature Contour in frequency-radial position space at fixed axial location z = 4 m B θ (ω,r) T i = 0 T i = 1eV Wave frequency scaled to Neon cyclotron frequency ω Ω Ne Ω ii Cold Propagation gap Ω He IBW-like propagation bands between harmonics of Neon cyclotron frequency Ω Ne 8 cm Radial position across magnetic field Typical LAPD parameters N e =10 12 cm -3 ; B 0 = 750G ; T e = 5 ev; 50%He-50%Ne; a = 1 cm

7 Comparison of Spatial Pattern (z, r) for Different Frequencies B 0 Contour of B θ (ω, z,r) for fixed frequencies 1.8Ω Ne 2.2Ω Ne 3.2Ω Ne A B C z T i = 1eV 50% He-50%Ne 10 meters T i = 0 100% He 8 cm Radial position across magnetic field Typical LAPD parameters N e =10 12 cm -3 ; B 0 = 750G ; T e = 5 ev; a = 1 cm r

8 Comparison of Spatial Phase-Pattern (z, r) for Different Frequencies B 0 z Contour of arg( B θ (ω, z,r) ) for fixed frequencies 1.8Ω Ne 2.2Ω Ne 3.2Ω Ne A B C T i = 1eV 50% He-50%Ne 10 meters T i = 0 100% He 8 cm Radial position across magnetic field r Typical LAPD parameters N e =10 12 cm -3 ; B 0 = 750G ; T e = 5 ev; a = 1 cm

9 Effect of Increasing Ion temperature Frequency dependence of B θ (ω,r,z) at a fixed position z = 4 meters, r = 3 cm 5 ev Magnitude of azimuthal magnetic field 1 ev T i = 0 Scaled frequency ω Ω Ne Typical LAPD parameters N e = cm -3 ; B 0 = 750G ; T e = 5 ev; a = 1 cm; 50%He-50%Ne

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11 Changing concentration ratio Helium/Neon mix 30% Helium 70% Neon 50% Helium 50% Neon Position across magnetic field Position across magnetic field Frequency dependence of magnetic field at z = 4.8 m and r= 2 cm ω Ω Ne

12 Measured frequency-radial dependence at fixed z = 4.8 m of wave magnetic field Helium band C Ω He 2π 50%He-50%Ne Gap Neon band B A Ω Ne 2π A Decay as 1 r Magnitude of wave magnetic field B C Radially extended Distance across magnetic field 12

13 Evidence of IBW-like features ω Ω Ne Spectral evolution ( ω,t) of wave magnetic field at fixed position Ω He = 5Ω Ne 50%He-50%Ne ω Ω Ne

14 Essential Physics--III Frequency ω and k are set by source Axial cut-off occurs when ε = 0 Since ω ii B 0 (z) For cold ions at ω = ω 2 p1ω ω 2 2 p 2 Ω 1 ω 2 2 = ω p1 + ω ii p 2 Waves can be reflected from a magnetic field ramp Wave Reflection Port 22 Port m 7.3 m 14

15 Effect of a magnetic step in a two ion plasma Experimental configuration Wave is launched in low field side With magnetic step Lower amplitude and no spreading due to evanescence Uniform field at 750 G 15

16 A resonator can be achieved in a magnetic well RF antenna B, z x Plasma: 17m x 60cm diam. Cathode Anode Z=512cm Z=128cm Z=0 Port 11 Port 23 Port 27 Magne8c probes H-He plasma 16

17 Theoretical Model 1) Approximate experimental magnetic well by two uniform regions connected by linear ramp Model 2) Solve analytically for Green s function Experiment J z 3) Use Green s function to obtain driven response by straight antenna current 4) Calculate driven magnetic field as a function of driver frequency Axial Position 17

18 Basic equations in cylindrical geometry (r, z) x L/2, plasma radius 2 E r z 2 E z = ε ε 1 k 2 k 0 2 ε ( k 2 k 2 0 ε )E r = k S z k 2 0 ε z E S z k r z k 0 ω c z, B 0 S 4π c ik 0 j B ϕ = ik k 0 (k 2 k 0 2 ε ) S z + ik 0 ε E r k 2 k 2 0 ε z ε = 1 ω ω + iν e Approximate antenna by a line current source at frequency ω 2 ω pe ( ) j z ( r,z,t ) = j Θ(z a ) Θ(z a 0 ( ) 1 2 )e iωt x < R 0 otherwise j z (k,z,t) = Rj 0 k J 1 ( k R)e iωt ( Θ(z a 1 ) Θ(z a 2 )) J z S z z δ(z a 1) δ(z a 2 ) l 2 l 1 a 1 a 2 18 z, B 0

19 Matching piecewise analytic solutions at 6 axial boundaries Solution for Fourier component of electric field E x (k,z) Outside well Reflection layer Left antenna E x (k,z) = Right antenna Reflection layer Outside well C 1 e k 2(z +l 2 ) z < l 2 C 2 Ai( -α(z + z 0 )) + C 3 Bi -α(z + z 0 ) C 4 e ik 1 (z a ) + C 5 e ik 1 (z a) l 1 < z < a C 6 e ik 1 (z a ) + C 7 e ik 1 (z a) a < z < l 1 C 2 Ai( α(z - z 0 )) + C 3 Bi( α(z - z 0 )) l 1 < z < l 2 C 10 e k 2 (z l 2 ) z > l 2 ( ) l 2 < z < l 1 Relate B to E r through Faraday s Law, and invert the Hankel transform using antenna spectrum 0 B ϕ (r,z,ω) = Rj 0 k J 1 ( k R) B ϕ (k,z)j 1 ( k r)k dk 19

20 Eigenfunction of Lowest-Frequency Trapped Mode at 568 khz Theory Real Part Model Magnetic Field H-He plasma Imaginary Part Axial Position 20

21 Dependence of trapped mode frequency on concentration ratio Theory First mode H-He Plasma Second mode Experimental Values See Fig Frequency (khz) 1250G 3 ω ii 2π Ω He 2π 750G Ratio of hydrogen density to electron density 21

22 Resonator eigenmodes excited by a current pulse in a magnetic well B 0 Wave trapping occurs by reflection at ion-ion hybrid resonance ω = ω ii Re Im B In 50%H - 50%He plasma ω = ω ii Temporal response Wavelet analysis Pulse f ii Trapped modes 22

23 Magnetic field spectra measured inside the magnetic well η H = 0.75 µ = 0.3 Frequency (khz) 23

24 Magnetic field spectra measured outside the magnetic well η H = 0.75 µ = 0.3 Frequency (khz) 24

25 Effect of decreasing hydrogen density (at fixed electron density) on magnetic field spectra inside the magnetic well z=128cm 1 1 Magnetic Field Magnitude, B y a.u. 2 3 Denotes Resonant Frequency value shown In Fig. 15. H-He Plasma 25

26 Perspective on ion-ion hybrid Alfvén wave resonator Experimentally have demonstrated that a magnetic step prevents wave penetration into high-field side --a necessary condition Pulsed excitation in a magnetic well shows formation of trapped eigenmodes with low Q values Key issues: How large is the dissipation near the ion-ion hybrid reflection layer? Can an ion beam or a plasma current trigger maser behavior? Nonlinear interaction with ions and electrons 26

27 Extra Slides 27

28 Effect of anomalous damping at reflection layer on spectrum an effective imaginary part is added to ε near reflection point Theory Trapped Waves Magnitude of wave magnetic field ( ω ii ) Out 2π H-He plasma ( Ω He ) Out 2π No damping Frequency (khz) 28