1. Rotating Wall/ Centrifugal Separation John Bollinger, NIST-Boulder Outline ● Penning-Malmberg trap – radial confinement due to angular momentum ● Methods for adding (or removing) angular momentum ● Energy input (heating) of rotating wall ● Experimental rotating wall examples: o UCSD Mg+ and e- experiments o Danielson/Surko strong drive regime o NIST no slip o Other examples (if time) ● Centrifugal separation o Condition for separation (1981 O’Neil manuscript) o Examples from experiments at NIST o Other experimental examples (electron/anti-proton) Please ask questions !!

2. Penning-Malmberg trap – radial confinement due to angular momentum ● axial confinement ↔ conservation of energy ● radial confinement ↔ conservation of angular momentum O’Neil, Dubin, UCSD

3. Radial expansion (or spin-down) due to asymmetries From T.B. Mitchell et al., in Trapped Charged Particles and Fundamental Physics (1999), p. 309. ● For laser-cooled plasmas in NIST Penning trap (R p << R trap ): Critical asymmetry produced by (B field)-(trap symmetry axis) misalignment ● B-field and trap symmetry axis aligned to better than 0.01 o by minimizing zero-frequency mode excitation r 2r o 2z o rr rotation frequency determined from plasma shape

4. Methods for adding (or removing) angular momentum 1.Sideband drive techniques/ axialisation (see January 16 presentation by Segal) quadrupole drives at ω z +ω m or Ω c =(Ω c -ω m )+ω m (with damping on ω z, Ω c ) single particle techniques that work well at low space charge 3. Rotate the trap - more practically, apply a rotating electric field asymmetry Rotating wall perturbations: 240 o 120 o 360 o 240 o 120 o 300 o 240 o 180 o 120 o 60 o m=2 m=1 2. Radiation pressure from a laser (laser torque) x y laser beam rr plasma boundary in x-y plane

6. Work due to rotating wall under steady state conditions ambient torques determine energy input (heating) due to the rotating wall application of the rotating wall requires cooling !! Can the applied torques and cooling be sufficiently strong for the rotating wall to work?

7. Rotating Wall/ Centrifugal Separation John Bollinger, NIST-Boulder Outline ● Penning-Malmberg trap – radial confinement due to angular momentum ● Methods for adding (or removing) angular momentum ● Energy input (heating) of rotating wall ● Experimental rotating wall examples: o UCSD Mg+ and e- experiments o Danielson/Surko strong drive regime o NIST no slip o Other examples (if time) ● Centrifugal separation o Condition for separation (1981 O’Neil manuscript) o Examples from experiments at NIST o Other experimental examples (electron/anti-proton)

8. UCSD Mg + and e - experiments PRL 78, 875 (1997); PRL 81, 4875 (1998); POP 7, 2776 (2000) ● e - cyclotron cooling; weak Mg + -neutral cooling (0.1 s -1 ) Central density compression by RW coupling to modes ● Strong torques applied by RW coupling to modes

9. UCSD Mg + and e - experiments PRL 78, 875 (1997); PRL 81, 4875 (1998); POP 7, 2776 (2000) ● strong torques applied by RW coupling to modes ● significant compression observed with both e - and Mg + ● e - cyclotron cooling; weak Mg + -neutral cooling (0.1 s -1 ) ● steady state confinement for weeks

10. Danielson/Surko strong drive regime PRL 94, 035001 (2005); POP 13, 055706 (2006); PRL 99, 135005 (2007) steady density vs applied RW frequency weak wall (0.1 V) vs strong wall (1.0 V) ● weak wall (0.1 V) compression at distinct frequencies, consistent with coupling to modes 1 V 0.1 V

11. Danielson/Surko strong drive regime PRL 94, 035001 (2005); POP 13, 055706 (2006); PRL 99, 135005 (2007) ● weak wall (0.1 V) compression at distinct frequencies, consistent with coupling to modes steady density vs applied RW frequency weak wall (0.1 V) vs strong wall (1.0 V) 1 V 0.1 V ● critical drive strength observed

12. NIST phase-locked rotating wall Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998) ● 10 2 <N<10 6 laser-cooled Be + ions ● T < 10 mK ● rotating wall applied uniformly across axial extent of plasma !!

13. NIST phase-locked rotating wall Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998) time-averaged Bragg scatteringstrobed ● 10 2 <N<10 6 laser-cooled Be + ions ● T < 10 mK ● rotating wall applied uniformly across axial extent of plasma !! ● in steady state rotating wall and plasma (crystal) rotation are phase coherent

14. NIST phase-locked rotating wall Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998) top-view image of a planar crystal showing distortion of the radial boundary with an ● Plasma shape is a tri-axial ellipsoid; rotating boundary applies torque; shear forces in crystal transmit forces to interior

15. Tutorial problem: prove this NIST phase-locked rotating wall Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998) ● impurity ions can couple a uniform electric field to internal degrees of freedom Monte Carlo simulation of equilibrium distribution of a two species plasma with 1000 particles (88% Be +, 12% m=26 u) Dubin 1998 centrifugal separation is asymmetric

16. Other examples of rotating wall compression ● mixed e - /pbar plasmas From Andresen et al., PRL 100, 203401 (2008) ● other examples ??

17. Rotating Wall/ Centrifugal Separation John Bollinger, NIST-Boulder Outline ● Penning-Malmberg trap – radial confinement due to angular momentum ● Methods for adding (or removing) angular momentum ● Energy input (heating) of rotating wall ● Experimental rotating wall examples: o UCSD Mg+ and e- experiments o Danielson/Surko strong drive regime o NIST no slip o Other examples (if time) ● Centrifugal separation o Condition for separation (1981 O’Neil manuscript) o Examples from experiments at NIST o Other experimental examples (electron/anti-proton)

18. Condition for centrifugal separation Consider two species q 1,m 1 and q 2, m 2 thermal equilibrium only difference is centrifugal potential ● Centrifugal separation is complete if: T.M. O’Neil, Phys. Fluids 24, 1447 (1981) ● Centrifugal separation important if:

19. Observations of centrifugal separation ● conditions for centrifugal separation readily satisfied with laser cooling ● Larson et al., PRL 57, 70 (1986) – sympathetically cool Hg + ions with laser-cooled Be ++ B B ● “missing volume” in laser cooled plasmas ● other laser-cooled plasma examples Be + -ion Imajo et al., PRA 55, 1276 (1997) Gruber et al., PRL 86, 636 (2001) Be + - e + Jelenkovic et al., PRA 67, 063406 (2003)

20. ● Andresen, et al., PRL 106, 145001 (2011). measured separation directly though imaging 1 T3 T Centrifugal separation with e - and pbar ● Gabrielse, et al., PRL 105, 213002 (2010). measured pbar radius looking for pbar loss when B=3.7 T ramped to 1 T measured time scale for separation to occur !! Add pbar slug to center of e - plasma

21. An interesting tutorial problem 9 Be +, 27 Al 3+ laser-cooled Be + sympathetically cools 27 Al 3+ a strongly coupled 2-component plasma ?? Calculate the rotation frequency ω r required for mixing of the 9 Be +, 27 Al 3+ species at a temperature of 10 mK? m Be = 8.942m p m Al = 26.772m p R p = 1 mm