Ion-Induced Instability of Diocotron Modes In Magnetized Electron Columns

1. UCSD Physics Ion-Induced Instability of Diocotron Modes In Magnetized Electron Columns Andrey Kabantsev University of California at San Diego Physics Department Nonneutral Plasma Physics Group • http://sdpha2.ucsd.edu/ , September 17, 2009

2. UCSD Physics OUTLINE Introduction to nonneutral plasmas. The physics of confinement. Diocotron modes. Genesis, (negative) energy and stability. Breaking the cylindrical and charge symmetries. Ion-induced instability of diocotron modes in electron plasmas. Ways to mitigate/suppress the ion-induced instability. A broader perspective on nonneutral plasmas. Conclusions. Final take-home message.

3. UCSD Physics Nonneutral plasmas are confinedby static electric and magnetic fields in a Penning-Malmberg trap R Cylindrical symmetry, single sign species => long confinement time

4. UCSD Physics Exceptional particle confinement properties less than 1% of the particles can ever move out to the wall, while more than 99% of the particles are confined forever (weeks in the experiments) Fast cyclotron radiation cooling + cryogenic walls Ultracold plasma (Coulomb) crystals with laser cooling of ions

5. UCSD Physics Diocotron waves

6. UCSD Physics Resistive wall destabilization of diocotron waves W.D. White, J.D. Malmberg and C.F. Driscoll "Resistive Wall Destabilization of Diocotron Waves," Phys. Rev. Lett. 49, 1822

7. (Spatial) Landau Mode Damping Damping is the spiral wind-up (phase mixing) of the density perturbation near the critical radius rc, where the fluid rotation rate wR(r) equals the wave phase rotation rate w/m resonance condition wR(rc) = w/m, No damping for “top-hat” n(r) profile Damping for a diffused n(r) profile wR(r) wR(r) w/m w/m n(r) n(r) rc rc spatial (r, R = /m velocity (, z)  = /k

8. UCSD Physics Mode Damping from rotational pumping B. Cluggish and C.F. Driscoll "Transport and Damping from Rotational Pumping in Magnetized Electron Plasmas," Phys. Rev. Lett. 74, 4213 (1995)

9. UCSD Physics Inevitable Wall Imperfections  Broken Cylindrical Symmetry  Drag of Rotating Plasmas (Negative Torque) on Static (or Slow Rotating) Asymmetries  Plasma Expansion and Heating ??????????????????????????? But a Faster Rotating Asymmetry Introduces the Positive Torque  Inward Particle Transport (Pinch), Accelerated Plasma Rotation (Still Leads to Plasma Heating)  Practically Infinite Confinement Time

10. UCSD Physics Compression of Electron Cloud by Rotating Wall (Surko’s Group)

11. UCSD Physics Compression of Antiproton Clouds by Rotating Wall (ALPHA Collaboration)

12. UCSD Physics  oppositely charged particles can move together to the wall still conserving P  From No Instabilities to Possible Diocotron Instabilities

13. UCSD Physics

14. G1 L2 H3 S4 G5 H6 S7 G8 H9 G10 B Rw fE Plasma -100 V -100 V UCSD Physics central density: n0  1.5107 cm-3 central potential: 0  – 30 V plasma radius: Rp  1.2 cm (RW= 3.5 cm) equilibrium temperature: T1 eV (D Rp/6) magnetic field: B≤ 20 kG EB rotation frequency: fE(B)  0.1 MHz (2kG/B) axial bounce frequency: fb(T)  0.6 MHz e–e collision frequency: ee(n,T)  160 sec-1 neutral pressure: P 10-11 Torr Pure electron plasma is contained in (up to) ten electrically isolated cylinders, with the cylinders S4 and S7 divided into up to 8 azimuthal sectors to excite, manipulate and detect various m  0 modes. Axial plasma confinement is provided by -100 V on the end cylinders. Radial confinement is provided by the axial magnetic field B. Plasma density z-integrated 2D-distribution n(r, ) is measured by instantaneous grounding the end cylinder, thereby allowing the plasma to stream onto a phosphor screen with attached CCD camera.

15. UCSD Physics Single-Pass Ion Beam center of charge R r  d center of trap electron column H2+ ***********************************

16. UCSD Physics Typical Experimental Procedure: seed the mode, suppress the others, inject ions, watch the growth Modulated Ion Injection (1:15) d1 D1 /RW f1(t) 1  1.5sec-1 f1 [kHz] f1(t), 1(t), Ne(t) i = i+ /eNe f1 = f1Ni /Ne i = i-1f1/f1 f1  2.2Hz 1  0.1sec-1 time [sec]

17. UCSD Physics B-dependence of the single-pass m - I+= 15pA - I+= 43pA B [kG]

18. UCSD Physics What if we inject an electron beam instead? 1 = -1.48s-1 Ie~ A Electron Beam Does Suppress Diocotron Waves !

19. UCSD Physics Double-Well(Nested)Traps The double-well traps can be tried to confine particles with the opposite signs of electric charge. In particular, they have been used recently at CERN to produce “anti-hydrogen” pairs. +50 V -20 V 0 V -20 V +50 V (z) However, the powerful constraint is now broken. Is there a problem with the modes stability ?

20. UCSD Physics Schematic of the Double-Well (Nested) Trap Experiment Le  53 cm Lend 14 cm Rw = 3.5 cm In a double-well trap the bounce-averagedEBdrift velocities of ions and electrons in diocotron perturbations nm are not equal. This leads to charge separation in nm and instability of the modes. EB H2+  B e- ½Lend ½Lend Le +V -V -V +V

21. Images of Ion-Induced Instabilities in a Double-Well Trap Experiments with partially neutralized electron plasma in the double-well trap show that the diocotron modes do become unstable ! UCSD Physics m = 2 m = 3 The modes shown here are called the m = 2 and m = 3 diocotron modes. The m = 1 diocotron mode is just a rigid off-axis spiraling of plasma column.

22. UCSD Physics Trapped(Multi-Pass)Ions Schematic of Ion Drift Trajectories in the Electron Column Diocotron Frame

23. UCSD Physics Exponential growth of the m = 1 diocotron mode over two decades in linear regime (d<dcr << 1) d D/RW 1  0.75sec-1 Time [sec]

24. Example of end /bncdependence untrapped dD/Rw ions trapped by H9 by Vcol by Vcol by H9 Time [sec] UCSD Physics

25. UCSD Physics Growth rate as a function of m - number m = 2 d q trapped untrapped untrapped m = 1 Time [sec]

26. UCSD Physics Growth rate as a function of the space-charge neutralization factor trapped -1 [sec-1] f1 [kHz] Time [sec]

27. UCSD Physics Growth rate as a function of the space-charge neutralization factor

28. UCSD Physics CONCLUSIONS *** In the case of fast transiting ions the growth rate of diocotron modes *** is relatively small and drops strongly with B *** In the case of slow trapped ions the growth rate of diocotron modes *** is defined by the neutralization (space-charge compensation) level solely, and thus may be very dangerous *** There are various stabilization and damping techniques, out of which *** the most effective has to be chosen according to plasma and trap parameters *** Rotating wall technique might be used to compensate the radial transport *** caused by the mode damping processes *In this presentation some illustrations from C.Surko (UCSD), J.Fajans (USB), NIST and ALPHA groups have been used.

29. Final Take-Home Message Pure electron (or ion) plasmas are simple objects with exceptional confinement properties. Introduction of particles with an opposite signof electric charge gives the way for diocotron modes to become unstable. Instability of diocotron modes is well controllable if one knows what to trade in. UCSD Physics