Transcript Rotating Wall

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 !!
𝜑 = constant
𝜔𝑟
𝜔𝑤𝑎𝑙𝑙
Penning-Malmberg trap – radial confinement due to angular momentum
● axial confinement ↔
conservation of energy
● radial confinement ↔
conservation of angular momentum


P   mv j  qA (r j ) r j
j

qB
Br
2
r
for
A
(
r
)

and B large

j

2 j
2
O’Neil, Dubin, UCSD
dP
0 
dt
r
2
j
 constant
j
Axial asymmetries produce increases in
𝑗 𝑟𝑗
2
Radial expansion (or spin-down) due to asymmetries
From T.B. Mitchell et al., in Trapped Charged Particles and Fundamental Physics (1999), p. 309.
rotation frequency determined
from plasma shape
2zo
r
r
2ro
● For laser-cooled plasmas in NIST Penning trap (Rp << Rtrap):
Critical asymmetry produced by (B field)-(trap symmetry axis) misalignment
● B-field and trap symmetry axis aligned to better than 0.01o by minimizing
zero-frequency mode excitation
Methods for adding (or removing) angular momentum
1. Sideband drive techniques/ axialisation (see January 16 presentation by Segal)
quadrupole drives at ωz+ωm or Ωc=(Ωc-ωm)+ωm (with damping on ωz , Ωc )
y
single particle techniques that work well at low space charge
laser beam
2. Radiation pressure from a laser (laser torque)
plasma boundary
in x-y plane
x
3. Rotate the trap
- more practically, apply a rotating electric field asymmetry
Rotating wall perturbations:
𝑉𝑠𝑒𝑐𝑡𝑜𝑟 = 𝑉𝑊𝑎𝑙𝑙 sin 𝜔𝑑𝑟𝑖𝑣𝑒 𝑡 + 𝜙
m=1
60o
𝜙 =0o
300o
120o
m=2
120o
240o
𝜔𝑤𝑎𝑙𝑙 = 𝜔𝑑𝑟𝑖𝑣𝑒
𝜙 =0o
240o
240o
𝜔𝑤𝑎𝑙𝑙
𝜔𝑤𝑎𝑙𝑙
180o
r
360o
120o
𝜔𝑤𝑎𝑙𝑙 = 𝜔𝑑𝑟𝑖𝑣𝑒 /2
𝑚𝜃 = 2 rotating wall potential simulation
- Brian Sawyer, NIST
Work due to rotating wall
Τ𝑎 = ambient torque due to field errors , background gas collisions, ..
Τ𝑤𝑎𝑙𝑙 = torque applied by the rotating electric field
● Τ𝑤𝑎𝑙𝑙 > Τ𝑎 and 𝜔𝑤𝑎𝑙𝑙 > 𝜔𝑟 ⇒
𝜔𝑟 increases
● steady state confinement requires Τ𝑤𝑎𝑙𝑙 = Τ𝑎
Work due to rotating wall 𝜔𝑤𝑎𝑙𝑙 Τ𝑤𝑎𝑙𝑙 = 𝜔𝑤𝑎𝑙𝑙 Τ𝑎
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?
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)
𝜑 = constant
𝜔𝑟
𝜔𝑤𝑎𝑙𝑙
UCSD Mg+ and e- experiments
PRL 78, 875 (1997); PRL 81, 4875 (1998); POP 7, 2776 (2000)
Central density compression by RW coupling to modes
𝑚𝜃 = 1
● 3× 109 electrons or 109 Mg+ ions
● e- cyclotron cooling; weak Mg+-neutral cooling (0.1 s-1)
● 𝑚𝜃 = 1 or 𝑚𝜃 = 2 rotating wall applied near ends of plasma
● Strong torques applied by RW coupling to modes
UCSD Mg+ and e- experiments
PRL 78, 875 (1997); PRL 81, 4875 (1998); POP 7, 2776 (2000)
● 3× 109 electrons or 109 Mg+ ions, B=4 T
● e- cyclotron cooling; weak Mg+-neutral cooling (0.1 s-1)
● 𝑚𝜃 = 1 or 𝑚𝜃 = 2 rotating wall applied near end of plasma
● strong torques applied by RW coupling to modes
● significant compression observed with both e- and Mg+
● steady state confinement for weeks
● non-zero slip 𝜔𝑤𝑎𝑙𝑙 > 𝜔𝑟 ; 𝜔𝑤𝑎𝑙𝑙 ~ plasma mode frequency coupling to the rotating wall
● maximum compression (density 𝑛0 ~109 cm-3) limited by 𝑛0 /𝑛0
𝑏𝑘𝑔
∝ 𝑛0 2 and heating
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)
● ~109 e-, B=5 T, e- cyclotron cooling Γ𝑐 ~6 s-1
● 𝑚𝜃 = 1 rotating wall applied near end of plasma
● weak wall (0.1 V) compression at distinct frequencies,
consistent with coupling to modes
● strong wall (1 V) compression at all frequencies,
no apparent slip 𝜔𝑟 ≅ 𝜔𝑤𝑎𝑙𝑙 ‼
1V
0.1 V
Danielson/Surko strong drive regime
PRL 94, 035001 (2005); POP 13, 055706 (2006); PRL 99, 135005 (2007)
𝑓𝑤𝑎𝑙𝑙 = 6 MHz
steady density vs applied RW frequency
weak wall (0.1 V) vs strong wall (1.0 V)
● ~109 e-, B=5 T, e- cyclotron cooling Γ𝑐 ~6 s-1
● 𝑚𝜃 = 1 rotating wall applied near end of plasma
● weak wall (0.1 V) compression at distinct frequencies,
consistent with coupling to modes
● strong wall (1 V) compression at all frequencies,
no apparent slip 𝜔𝑟 ≅ 𝜔𝑤𝑎𝑙𝑙 ‼
1V
0.1 V
● critical drive strength observed
● maximum density 𝑛0 ~3 × 109 cm-3
● strong drive regime characterized by 𝑛0 /𝑛0
𝑏𝑘𝑔
independent of 𝑛0 , 𝜈𝑒𝑒 > 𝑓𝑏
● increased cyclotron cooling, lower outward transport ⇒ enabled access to strong drive regime
NIST phase-locked rotating wall
𝑚𝜃 = 2
𝜔𝑟 ⟶
Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998)
𝜔𝑤𝑎𝑙𝑙 ⟶
● 102<N<106 laser-cooled Be+ ions
● T < 10 mK
● compression and no slip observed with
both 𝑚𝜃 = 2 and 𝑚𝜃 = 1 walls
● rotating wall applied uniformly across axial
extent of plasma !!
𝑚𝜃 = 1
NIST phase-locked rotating wall
Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998)
time-averaged Bragg scattering
strobed
𝑚𝜃 = 2
𝑚𝜃 = 1
● 102<N<106 laser-cooled Be+ ions
● T < 10 mK
● compression and no slip observed with
both 𝑚𝜃 = 2 and 𝑚𝜃 = 1 walls
● rotating wall applied uniformly across axial
extent of plasma !!
● in steady state rotating wall and plasma
(crystal) rotation are phase coherent
NIST phase-locked rotating wall
Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998)
● Torque mechanism for 𝑚𝜃 = 2 wall with
crystalized plasma easy to understand
● 𝑚𝜃 = 2 wall changes the potential in the
rotating frame


  
m z2 2
1
qrot (r , z ) 
z   r2 ,   r c2 r 
2
z
2

qrot ( x, y, z ) quad wall
  Vwall

m z2 2

z     x 2      y 2
2

● Plasma shape is a tri-axial ellipsoid;
rotating boundary applies torque;
shear forces in crystal transmit forces to interior

top-view image of a planar crystal showing
distortion of the radial boundary with an
NIST phase-locked rotating wall
Huang et al., PRL 80, 73 (1998); POP 5, 1656 (1998)
● Why does the 𝑚𝜃 = 1 (dipole) wall work??
● A uniform electric field only drives a center-of-mass
motion for a single species plasma in a quadrupole trap
𝜙𝑇 =
𝑚𝜔𝑧 2
2
𝑧2
−
𝑟2
2
Tutorial problem: prove this
● 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
Other examples of rotating wall compression
● mixed e-/pbar plasmas
From Andresen et al., PRL 100,
203401 (2008)
● other examples ??
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)
𝜑 = constant
𝜔𝑟
𝜔𝑤𝑎𝑙𝑙
Condition for centrifugal separation
T.M. O’Neil, Phys. Fluids 24, 1447 (1981)
Consider two species q1,m1 and q2, m2
thermal equilibrium
⇒
 q
n1 (r , z )  exp  1
 k BT

r 2 m1 2 r 2  
 p (r , z )  T (r , z )  r B  r  
2 q1
2 

 q2
n2 (r , z )  exp 
 k BT

r 2 m2 2 r 2  
r  
 p (r , z )  T (r , z )  r B 
2
q
2 
2

both species evolve to same 𝜔𝑟
only difference is
centrifugal potential
● Centrifugal separation important if:
[centrifugal force difference]×[size of plasma] > kBT
e
m1 m2 2

 r R p  R p  k BT ,
q1 q2

e 1.6 10 19 C

R p  k BT m1 m2 r R p   cen
2
● Centrifugal separation is complete if: D   cen
if q1  q2  e , then centrifugal separation condition can be written :
m1  m2 v2  k BT
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
● “missing volume” in laser cooled plasmas
● other laser-cooled plasma examples
B
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)
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
● Andresen, et al., PRL 106, 145001 (2011).
measured separation directly though imaging
measured time scale for separation to occur !!
Add pbar slug to center of e- plasma
1T
3T
An interesting tutorial problem
9Be+, 27Al3+
laser-cooled Be+ sympathetically cools 27Al3+
a strongly coupled 2-component plasma ??
Calculate the rotation frequency ωr required for mixing of the 9Be+, 27Al3+ species
at a temperature of 10 mK?
mBe = 8.942mp
mAl= 26.772mp
Rp= 1 mm