1. 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/ UCSD Physics, September 17, 2009

2. 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. UCSD Physics

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

4. Exceptional particle confinement properties Fast cyclotron radiation cooling + cryogenic walls Ultracold plasma (Coulomb) crystals 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) 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"Resistive Wall Destabilization of Diocotron Waves,"

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

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

9. Inevitable Wall Imperfections  Broken Cylindrical Symmetry  Drag of Rotating Plasmas (Negative Torque) on Static (or Slow Rotating) Asymmetries  Plasma Expansion and Heating ??????????????????????????? UCSD Physics 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. Compression of Electron Cloud by Rotating Wall (Surko’s Group) UCSD Physics

11. 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. 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. B RwRw fEfE G1 L2 H3 S4 G5 H6 S7 G8 H9 G10 Plasma -100 V central density: n 0  1.5  10 7 cm -3 central potential:  0  – 30 V plasma radius: R p  1.2 cm (R W = 3.5 cm) equilibrium temperature: T  1 eV ( D  R p /6) magnetic field: B ≤ 20 kG E  B rotation frequency: f E (B)  0.1 MHz (2kG/B) axial bounce frequency: f b (T)  0.6 MHz e–e collision frequency: ee (n,T)  160 sec -1 neutral pressure: P  10 -11 Torr UCSD Physics

15.  RR H2+H2+ electron column d center of charge center of trap rr ***********************************

16. UCSD Physics time [sec] f 1 [kHz ] d 1  D 1 /R W  1  0.1sec -1  1  1.5sec -1  f 1  2.2Hz f1(t)f1(t) f 1 (t),  1 (t), N e (t) i = i + /eN e  f 1 = f 1 N i /N e  i = i -1  f 1 /f 1 Modulated Ion Injection (1:15) Typical Experimental Procedure: seed the mode, suppress the others, inject ions, watch the growth

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

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

19. UCSD Physics 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)(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 +V -V H 2 +  e-e- B EBEB LeLe ½L end L e  53 cm L end  14 cm R w = 3.5 cm In a double-well trap the bounce-averaged E  B drift velocities of ions and electrons in diocotron perturbations  n m are not equal. This leads to charge separation in  n m and instability of the modes.

21. 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. 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 !

22. UCSD Physics Schematic of Ion Drift Trajectories in the Electron Column Diocotron Frame

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

24. Time [sec] d  D/Rwd  D/Rw Example of  end /  bnc dependence untrapped ions trapped by V col by H 9 UCSD Physics

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

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

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

28. 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 UCSD Physics *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 sign of 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