9th international work shop on non -neutral plasmas

9th International Workshop on Non-Neutral Plasmas

Columbia University in the City of New York

June 16-20, 2008

ABSTRACTS

1

TUESDAY, 17 JUNE 2008

Session 1: Collective Modes and Transport Physics I Chair: C. Roberson, Office of Naval Research (Ret)

08:30-09:00 D. Dubin, Univ. of California San Diego

Theory and Simulations of Electrostatic Field Error Transport 8

09:00-09:30 M. Anderson, Univ. of California San Diego

Collisional Damping of Plasma Waves on a Pure Electron Plasma 9

09:30-09:50 M. Rome, University degli Studi Milano

Relativistic Effects on the Radial Equilibrium of Nonneutral Plasmas 10

Session 2: Collective Modes and Transport Physics II Chair: T. Pedersen, Columbia University

10:30-11:00 F. Anderegg, Univ. of California San Diego

Electron Acoustic Waves in Pure Ion Plasmas 11

11:00-11:20 Y. Yeliseyev, Kharkov Inst. of Physics and Tech.

Stability of a Nonneutral Plasma Cylinder Consisting of Magnetized Cold

Electrons and a Small Density Fraction of Ions Born at Rest: Nonlocal Analysis 12

11:20-11:40 D. Eggleston, Occidental College

Using Variable Frequency Asymmetries to Probe the Magnetic Field Dependence of

Radial Transport in a Malmberg-Penning Trap 13

11:40-12:00 R. Heidemann, Max-Planck Inst. for Extraterrestriche Physik

Heartbeat Instability in the PK-3 Plus Laboratory 14

Session 3A: Collective Modes and Transport Physics III Chair: H. Himura, Kyoto Inst. of Tech.

13:30-14:00 A. Kabantsev, Univ. of California San Diego

Trapped-Particle-Mediated Asymmetry-Induced Transport and Damping with

Quadrupole Separatrix Perturbations 15

14:00-14:20 Y. Kawai, Kyoto Univ.

Turbulent Cascade in Vortex Dynamics of Magnetized Pure Electron Plasmas 16

Session 3B: Beam Physics

14:20-14:50 E. Gilson, Princeton Plasma Physics Lab.

Overview of Intense Beam Simulation Experiments Performed Using the

Paul Trap Simulator Experiment (PTSX) 17

14:50-15:20 J. Wurtele, Univ. of California Berkeley

Brightness and Phase Space Constraints in Free-Electron Lasers 18

15:20-15:40 G. Maero, GSI, Darmstadt

Investigations on Cooling Mechanisms of Highly Charged Ions at HITRAP 19

2

Session 4: Poster Session I

16:00-18:00 Collective Modes and Transport, Beam Physics, Strongly Coupled and Dusty Plasmas

All speakers in sessions 1-6 are invited to present posters in this session. Posters can be put up

Monday evening or Tuesday morning and taken down on Wednesday during the lunch break.

(presenting author in bold)

F. Anderegg and C. Driscoll

Measurements of Correlation-Enhanced Collision Rates 20

G. Bettega, et al.

Excitation of High Order Diocotron Modes in the ELTRAP Device 21

M. Rome and I. Kotelnikov

Effect of a Weakly Tilted Magnetic Field on the Equilibrium of Nonneutral

Plasmas in a Malmberg-Penning Trap 22

K.N. Stepanov and Yu N. Yeliseyev

Drift Motion of Charged Particle in Electromagnetic Field of Magnetic Pumping

Under Cherenkov and Cyclotron Resonance Conditions 23

Yu N. Yeliseyev, et al.

Studying Nonneutral Plasma at Kharkov National University 24

M. Aramaki, et al.

Observation of String Ion Cloud in a Linear RF Trap 25

N. Shiga, W.M. Itano, and J.J. Bollinger

Spectroscopy of Ground State 9Be+ Ions in a 4.5 T Penning Trap 26

R. Heidemann, et at.

Solitary Rarefaction Wave in Three-Dimensional Complex Plasma 27

K. Nellissen, et al.

Structural Properties of Binary Colloidal Systems Confined in Quasi-

One-dimensional Channel 28

K. Nelissen, et al.

Dissipation in a 2D Classical Cluster 29

3

WEDNESDAY, 18 JUNE 2008

Session 5: Strongly Coupled and Dusty Plasmas I Chair: L. Schweikhard, Ernst-Moritz-Arndt-Universitat, Greifswald

08:30-09:00 M. Drewsen, Univ. of Aarhus

Ion Coulomb Crystals in RF Traps: Properties and Applications in Cavity QED 30

09:00-09:30 D. Porras, Max-Planck Inst. for Quantum Optics

Quantum Computation and Quantum Simulation with Coulomb Crystals 31

09:30-09:50 M. Rubin-Zuzic, Max-Planck Inst. fur Extraterrestriche Physik

PK-3 Plus - Investigation of Complex Plasmas on the International Space Station 32

Session 6: Strongly Coupled and Dusty Plasmas II Chair: D. Eggleston, Occidental College

10:30-11:00 S. Sturm, Johannes Gutenberg-Universitat Mainz

Investigation of Space-Charge Phenomena in Gas-Filled Penning Traps 33

11:00-11:20 M. Dietrich, Univ. of Washington

Barium Ions for Quantum Computation 34

11:20-11:40 R. Sutterlin, Max-Planck Inst. fur Extraterrestriche Physik

Lane Formation in Complex Plasmas 35

11:40-12:00 S. Apolinario, Universiteit Antwerpen

Melting Processes in Anisotropic Coulomb Balls 36

Session 7: Toroidal Plasmas Chair: T. O’Neil, Univ. of California San Diego

13:30-14:00 J. Marler, Aarhus Univ.

Achieving Long Confinement in a Toroidal Electron Plasma 37

14:00-14:30 H. Himura, Kyoto Inst. of Tech.

Recent Progress on Toroidal Non-neutral Plasmas Confined on Heliotron

Magnetic Surfaces 38

14:30-15:00 T. Pedersen, Columbia Univ.

Confinement and Transport in the CNT Stellerator 39

15:00-15:20 Q. Marksteiner, Columbia Univ.

Studies of a Parallel Force Balance Breaking Instability in a Stellerator 40

4

Session 8: Poster Session II

15.45-18:00 Toroidal Plasmas, Antimatter Physics, Ultracold Neutral Plasmas and Special Topics

All speakers in sessions 7-12 are invited to present posters during this session.

Posters can be put up during the lunch break on Wednesday and left up for the duration of the conference.

(presenting author in bold)

J.R. Danielson, T.R. Weber, and C.M. Surko

A Multicell Trap for Storage of Large Numbers of Positrons 41

A. Kurcz, A. Capolupo, and A. Beige

Inside Nature's Smallest Black Body 42

P. W. Brenner, et al.

Studies of Enhanced Confinement in the Columbia Non-neutral Torus 43

B. Durand de Gevigny, T.S. Pedersen, and A.H. Boozer

Numerical Studies of Transport in the Columbia Non-neutral Torus 44

P.C. Ennever, et al.

Computer Simulation of Ion Motion in CNT Using an Adams-Moulton Adaptive 45

Step Size Numerical ODE Solver

M. Hahn, et al.

Pure Electron Equilibrium and Transport Jumps in the Columbia Non-neutral Torus 46

M.R. Stoneking, Bao Ha, and J.P. Marler

Modeling Wall Probe Signals in a Toroidal Electron Plasma 47

J.A. Castro, H. Gao, and T.C. Killian

Fluorescence Spectroscopy and Ion Temperature Evolution in Ultracold Neutral Plasmas 48

D. Vrinceanu, G. S. Balaraman, and L. A. Collins

King Model for electrons in a finite size ultracold plasma 49

5

THURSDAY, 19 JUNE 2008

Session 9: Antimatter Physics I Chair: C. Surko, Univ. of California San Diego

08:30-09:00 H. Saitoh, Atomic Physics Lab., RIKEN

Radial Compression of a Non-neutral Plasma in a Non-uniform Magnetic 50

Field of a Cusp Trap

09:00-09:30 D. Le Sage, Harvard Univ.

First Antihydrogen Production within a Penning-Ioffe Trap 51

09:30-10:00 J. Fajans, Univ. of California Berkeley

First Attempts at Antihydrogen Trapping in ALPHA 52

Session 10: Antimatter Physics II Chair: C. F. Driscoll, Univ. of California San Diego

10:40-11:10 J. Danielson, Univ. of California San Diego

Attracting Fixed Points and Strong-Drive Compression of Single-Component Plasmas 53

11:10-11:40 T. Weber, Univ. of California San Diego

Creation of Finely Focused Beams from Single-Component Plasmas 54

11:40-12:00 N. Kuroda, Inst. of Physics, Univ. of Tokyo

Radial Compression of Antiproton Cloud for Production of Ultraslow Antiproton Beams 55

6

FRIDAY, 20 JUNE 2008

Session 11: Special Topics and Ultracold Neutral Plasmas I Chair: M. Drewsen, University of Aarhus

08:30-09:00 J. Petri, Centre d'etude des Environnements Terrestre et Planetaires

Electrodynamics of Neutron Star Magnetospheres: An Example of Non-neutral

Plasma in Astrophysics 56

09:00-09:30 E. Nikolaev, Inst. for Energy Problems of Chemical Physics, Moscow

Supercomputer Modeling of Ion Cloud Motion in Mass Spectrometers 57

09:30-10:00 G. Raithel, Univ. of Michigan

Plasma Dynamics and Recombination in a High-Magnetic Field Atom and Plasma Trap 58

Session 12: Special Topics and Ultracold Neutral Plasmas II Chair: J. Bollinger, National Inst. of Standards and Tech., Boulder

10:30-11:00 T. Killian, Rice Univ.

Expansion and Equilibration of Ultracold Neutral Plasmas 59

11:00-11:30 T. Pohl, Harvard Univ.

Low-temperature Atom Formation in Ultracold Neutral Plasmas 60

11:30-12:00 S. Rolston, Univ. of Maryland

Ultracold Plasma Expansion and Instabilities 61

12:00-12:30 C. Roberson, Office of Naval Research (Ret)

Non-neutral Plasma Physics at Twenty 62

7

Theory and Simulations of Electrostatic Field Error Transport*

Daniel H.E. Dubin

Univ. of California at San Diego Physics Dept., 9500 Gilman, La Jolla CA 92093

This talk will provide an overview of neoclassical transport theory and accompanying

experiments using nonneutral plasmas. Asymmetries in applied electromagnetic fields

are thought to dominate the loss processes observed in many nonneutral plasma

experiments. However, detailed measurements of asymmetry – induced transport

over several decades have not made very close contact with neoclassical theory.

In order to investigate why this might be the case, theory and simulations of

neoclassical transport have been developed specifically with nonneutral plasma

experiments in mind [1]. For simplicity, the magnetic field is assumed to be uniform

– transport is due to asymmetries in applied electrostatic fields. Idealized simulations

of the transport follow guiding centers in the given fields, neglecting collective effects

on the plasma evolution, but keeping collisions at constant rate !. Also, the Fokker-

Planck equation is solved in a local approximation, valid in the transport limit where

the asymmetry potential is small compared to the plasma temperature. This allows

determination of local transport coefficients that link dissipative radial particle,

momentum and energy fluxes to plasma rotation, parallel velocity, and temperature

and velocity gradients. Theory is found to agree with the simulations in all cases.

Three examples of increasing complexity are studied: a plasma column with periodic

boundary conditions, to which a sinusoidal asymmetry is applied; a finite length

column with a similar asymmetry; and a column to which a symmetric squeeze

potential is applied, creating trapped particle populations in the equilibrium. In the

first two cases, the transport displays the expected neoclassical behavior, breaking

into banana, plateau and fluid regimes. However, correct predictions require rather

precise knowledge of the applied fields. For example, the use of approximate periodic

boundary conditions in a finite length plasma is found to be a poor approximation in

the plateau regime. Also, when a squeeze is applied, new ! and ! "! transport

regimes are observed, similar to those predicted for neoclassical transport in

stellarators. Even small populations of trapped particles can completely change the

magnitude and scaling of the transport.

The talk will conclude with a discussion of outstanding theoretical questions, and

suggestions for further experiments.

* Work supported by National Science Foundation grant PHY-0354979 and

NSF/DOE grant PHY-0613740.

[1] D. Dubin, "Theory and Simulations of Electrostatic Field Error Transport" Phys.

Plasmas (2008), to be published.

8

Collisional Damping of Plasma Waves on a Pure Electron Plasma*

M. W. Anderson and T. M. O’Neil

University of California, San Diego

The collisional damping of electron plasma waves (or, more precisely, Trivelpiece-Gould

waves) on a pure electron plasma column is discussed. The damping in a pure electron

plasma differs from that in a neutral plasma, since there are no ions to provide collisional

drag on the oscillatory motion of the electrons. A dispersion equation for the complex

wave frequency is derived from Poisson’s equation and the drift-kinetic equation with the

Dougherty collision operator—a Fokker-Planck operator that conserves particle number,

momentum, and energy and yet is analytically tractable. The dispersion equation spans

from weak collisionality to strong collisionality, matching onto results from fluid theory

in the latter limit. For phase velocity comparable to the thermal velocity, Landau

damping is recovered in the weakly collisional limit [1]. For larger phase velocity, where

Landau damping is negligible, the dispersion equation yields the simple formula [2]

])21)(9/101())(2/3(1)[/( 12 !"""# $$%&& iikkk Dpz for the complex wave frequency,

where p& is the plasma frequency, kz is the axial wavenumber, k is the total

wavenumber, D% is the Debye length, ' is the collision frequency, and ./ zpkk &'$ (

Note that in the weakly collisional regime, the damping rate is given by

,3/)(4)Im( 2Dk%'& !) which is suppressed from the collisional damping rate in a

neutral plasma [ 2/)Im( '& !) ] by the small factor 1)( 2**Dk% [3]. This suppression

reflects the conservation of electron momentum in the pure electron plasma. The

damping in the pure electron plasma results from bulk viscosity, which, in turn, arises

from collisional velocity scattering between parallel and perpendicular degrees of

freedom.

Recent damping measurements on cold Mg+ plasmas confirm the 2/1!T scaling predicted

by the above formula (for ),1**$ but the observed damping rate exceeds the predicted

rate by over an order of magnitude. The source of this discrepancy is currently being

investigated, both theoretically and experimentally.



[1] L. D. Landau, J. Phys. 10, 25 (1946).

[2] M. W. Anderson and T. M. O’Neil, Phys. Plasmas 14, 112110 (2007).

[3] A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456 (1958).

9

Relativistic effects on the radial equilibrium of nonneutral plasmas

M. Romé1, I. Kotelnikov

2 and R. Pozzoli

1

1I.N.F.N. Sezione di Milano and Dipartimento di Fisica,

Università degli Studi di Milano, Via Celoria 16, Milano, I-20133, Italy

2Budker Institute of Nuclear Physics, Lavrentyev Av. 11, Novosibirsk, 630090, Russia

Relativistic effects on the radial equilibrium of nonneutral plasmas confined in

cylindrical traps are analyzed for rigid and sheared modes of plasma rotation, both

with and without the presence of a coaxial inner charged conductor [1,2].

The changes with respect to the non-relativistic results are especially pronounced for

the fast rotational equilibrium solutions (when the frequency of the plasma azimuthal

rotation is close to the cyclotron frequency).

In the case of a solid plasma column the density profile turns out to be nearly

parabolic rather than stepwise as predicted by the non-relativistic theory. This

modification of the equilibrium density profile should be observable in experiments

similar to those performed by Theiss et al. [3].

In the case of an annular plasma column it is found that relativistic effects can limit its

outer radius. Analytical estimates of this maximum radius are found both for a rigid

plasma rotation and for the case of a uniform plasma density.

It is also observed that the Brillouin density limit is modified when the shielding of

the external magnetic field by the current associated with the plasma rotation becomes

significant and a class of sheared equilibria is found where the limit valid for the case

of rigid rotation can be overcome.

[1] I. Kotelnikov, M. Romé and R. Pozzoli, Phys. Lett. A 372, 1445 (2008).

[2] I. Kotelnikov, M. Romé and R. Pozzoli, Phys. Lett. A 372, 2450 (2008).

[3] A. J. Theiss, R. A. Mahaffey, A. W. Trivelpiece, Phys. Rev. Lett. 35, 1436 (1975).

10

!

"

#!

#"

$!

$"

%!

! !&" # #&"

f [k

Hz]

T [eV]

TG

EAW

mr=2

Electron Acoustic Waves in Pure Ion Plasmas*

F. Anderegg, C. F. Driscoll, D. H. E. Dubin and T. M. O’Neil


Electron Acoustic Waves (EAWs) are the low frequency branch of electrostatic plasma waves; these waves exist in neutralized plasmas [1], pure electrons [2] and pure ion plasmas. The EAWs typically have a phase velocity !!"#$% &!'" ( )*+ , quite low compared to typical plasma waves. Linear Landau damping would suggest that such slow phase velocity waves are strongly damped; but at finite wave amplitudes, trapping of particles at the phase velocity effectively flattens the distribution function. This forms a “BGK-like” state with weak damping.

Our experiments show that the small-amplitude dispersion relation for both fast (TG) and slow (EAW) plasma modes is in close agreement with kinetic theory of undamped waves [3,4]. However, the EAW waves seem to be inherently less frequency-determinate than the upper-branch plasma waves; the surprise here is that a moderate amplitude “off-resonant” drive readily modifies the velocity distribution so as to make the EAW mode resonant with the drive frequency.

At temperatures above the end of the EAW dispersion “thumb,” we find that moderate amplitude drives create resonant modes over a wide range of frequencies. With chirped frequency drive similar to the one used by the Berkeley group [5], the particle velocity distribution function suffers extreme distortion, and the resulting plasma wave is almost undamped with ! !" " #$#%.

Laser-Induced-Fluorescence measurements of the wave-coherent f (vz) clearly show particle trapping in the EAW mode, with trapping widths as expected from theory. These measurements also elucidate the unusual, “pressure-dominated” nature of the EAW: the net fluid velocities are small, because the electrostatic restoring force is almost totally balanced by the kinetic pressure.

* Work supported by NSF PHY-0354979 and NSF/DOE PHY-0613740. [1] D.S. Montgomery et al., Phys. Rev. Lett. 87, 155001 (2001). [2] A.A. Kabantsev, F. Valentini, and C.F. Driscoll, AIP Conf. Proc. 862, 13 (2006). [3] J.P. Holloway and J.J. Dorning, Phys. Rev. A 44, 3856 (1991). [4] F. Valentini, T.M. O'Neil and D.H.E. Dubin, Phys. Plas. 13, 052303 (2006). [5] W. Bertsche, J. Fajans and L. Friedland, Phys. Rev. Lett. 91, 265003 (2003); !! F. Peinetti et al., Phys. Plas. 12, 062112 (2005).

11

Stability of NonNeutral Plasma Cylinder Consisting of Magnetized

Cold Electrons and of Small Density Fraction of Ions Born at Rest:

NonLocal Analysis

Yu. N. Yeliseyev

Institute of Plasma Physics, National Science Center

“Kharkov Institute of Physics and Technology” Kharkov, Ukraine

In the report the non-local stability problem of the plasma cylinder, filled with a

"cold" magnetized rigidly rotating electrons, and with a small density fraction of ions,

is solved. The ions are supposed to be born at rest by ionization of a background gas.

They move collisionless in crossed fields. The radial electric field is caused by a space

charge of non-neutral plasma. In a strong electric field the ions perform radial

oscillating motion along strongly extended trajectories with so called “modified” ion

cyclotron (MIC) frequency i

! . Such plasmas are formed, for example, in plasma

lenses, in ion sources based on a Penning cell, in channels of electron and ion beams

(secondary plasmas). The treatment of plasma stability is based on the kinetic

consideration of ions. The equilibrium distribution function [1, 2], taking into account

the peculiarity of ion formation, is used. It possesses the features of both the

degenerate Fermi-Dirac distribution function and of “rigid rotor” one. The dispersion

equation for plasma natural frequencies is obtained analytically. It is valid within the

total admissible range of values of electric and magnetic fields. Normalized natural

frequencies /i

"# ! are computed for the basic azimuth mode 1m = , for the density

fraction of ions of atomic nitrogen / 0,01i e

f N n= = and are presented in graphic

form as dependences on parameter 2 22 /pe ce" " ( 2 20 2 / 1/(1 )pe ce f" "< < $ ). (Here

im" " "+# = $ ,

i"+ - is the “slow” rotation frequency of ions in crossed fields.)

The spectra of oscillations "# consist of the family of volumetric electron Trivelpiece-

Gould modes (TG) (their frequencies in crossed fields hit in the region of ion

frequencies) and of the families of MIC modes (their frequencies are located in a small

vicinity of harmonics of the MIC frequency i

! above and below the harmonic). The

modes TG become unstable at crossing with the MIC modes. The instability has a

resonant character. The lowest radial mode TG has a maximum growth rate at crossing

with a zero harmonic i

! ( max(Im / ) 0,074i

"# ! % ). The growth rates of MIC modes are

much less ( max(Im / ) 0,002i

"# ! <!

). Their instability has a threshold character.

The oscillations of small amplitude are clearly seen on some frequency dependencies

of MIC modes. They are similar to oscillations on dispersion curves of electron waves

in metals and are caused by the similarity of the equilibrium distribution function of

ions with the degenerate Fermi - Dirac distribution function.

The instabilities of TG and MIC modes take place mainly in the region of strong

radial electric field where the ions are unmagnetized and the non-local stability

analysis is necessary. Such analysis is given in the report. The obtained results give

the solution of the stability problem, discussed in [3], for a special case when the

plasma cylinder bounds with a metal and posses the volumetric natural modes only.

[1] Yu. N. Yeliseyev, in Non-Neutral Plasma Physics VI, edited by M. Drewsen,

U. Uggerhoj, H. Knudsen (AIP, New York, 2006), 862, 108-115.

[2] Yu. N. Yeliseyev, Plasma Phys. Rep. 32, 927-936 (2006).

[3] R.H. Levy, J.D. Daugherty and O. Buneman, Phys. Fl. 12, 2616-2629 (1969).

12

Using variable-frequency asymmetries to probe the magnetic field

dependence of radial transport in a Malmberg-Penning trap

D. L. Eggleston

Occidental College, Los Angeles, California, USA

A new experimental technique is used to study the dependence of asymmetry-induced

radial particle flux ! on axial magnetic field B in a modified Malmberg-Penning trap.

This dependence is complicated by the fact that B enters the physics in at least two

places: in the asymmetry-induced first order radial drift velocity vr=E"/B and in the

zeroth order azimuthal drift velocity v"=Er/B. To separate these, we employ the

hypothesis that the latter always enters the physics in the combination #-l#R, where

#R=v"/r is the column rotation frequency and # and l are the asymmetry frequency

and azimuthal mode number, respectively. Points where #-l#R=0 are then selected

from a ! vs r vs # data set, thus insuring that any function of this combination is

constant. When the selected flux !sel is plotted versus the density gradient, a roughly

linear dependence is observed, showing that this selected flux is diffusive. This linear

dependence is roughly independent of the bias of the center wire in our trap $cw.

Since in our experiment #R is proportional to $cw, this latter point shows that our

technique has successfully removed any dependence on #R and its derivatives, thus

confirming our hypothesis. The slope of a least-squares fitted line through the !sel vs

density gradient data then gives the diffusion coefficient D0 under the condition #-l#R

=0. Varying the magnetic field, we find D0 is proportional to B-1.33±0.05

, a scaling that

does not match any theory we know. These findings are then used to constrain the

form of the empirical flux equation. It may be possible to extend this technique to

give the functional dependence of the flux on #-l#R.

Supported by USDOE grant DE-FG02-06ER54882.

13

HEARTBEAT INSTABILITY UNDER

MICROGRAVITY CONDITIONS OBSERVED IN THE

PK-3 PLUS LABORATORY

Ralf J. Heidemann, Hubertus M. Thomas, Sergey K. Zhdanov,

Alexey V. Ivlev and Gregor E. Morfill

Max-Planck-Institut für extraterrestrische Physik

Giessenbachstraße 85748 Garching Germany

Vladimir E. Fortov, Vladimir I. Molotkov, Oleg F. Petrov,

and Andrey I. Lipaev

RAS - Institute for High Energy Densities, Izhorskaya 13/19,

Moscow, 127412, Russia

In many experiments that were performed with the PK-3 Plus

setup on board of the International Space Station the so

called heartbeat instability could be observed. Under

microgravity conditions the microparticles in a complex

plasma arrange themselves in a vast cloud that spreads nearly

all over the available inter-electrode space. In the middle of

the plasma chamber a void is often formed1,2

. The void is

completely free of particles. Under certain conditions the

complex plasma becomes unstable and rhythmically pulsates

in the radial direction3,4

. In given experiments the instability

has been observed in a wide parameter range. Measurements

where performed with MF particles of different diameters

from 6.81µm to 15µm in Argon as well as in Neon plasma at

different discharge powers. The gas pressure varies between

8Pa and 100Pa. The frequency of the observed oscillation

ranges from 0.8Hz to 7Hz. At the lower frequencies

oscillations are strongly nonlinear. The oscillation frequency

increases linearly with plasma power and with the neutral gas

pressure. The correlation of the particle motion and the

recorded plasma parameters is discussed.

Figure1. Visualization of microparticle oscillations affected

by the heartbeat instability

1. D. Samsonov and J. Goree, Phys. Rev. E 59, 1047 (1999).

2. A. Lipaev et. al., Phys. Rev. Lett. 98, 265006 (2007)

3. M. Kretschmer et. al., Phys. Rev. E 71, 056041 (2005).

4. M. Mikikian et. al., NJP 9, 268 (2007).

14

Trapped-Particle-Mediated Asymmetry-Induced Transport and

Damping with Quadrupole Separatrix Perturbations*

A. A. Kabantsev1, Yu. A. Tsidulko

2, C. F. Driscoll

1

1Univ. of California at San Diego Physics Dept., 9500 Gilman, La Jolla CA 92093

2Budker Inst. of Nuclear Physics, Novosibirsk, Russia 630090

Recent experiments show that weak quadrupole asymmetries added to a trapping

separatrix have large effects on asymmetry-induced transport and wave damping, as

suggested by recent theory work. Here, the pure electron plasma columns have a

weak trapping separatrix created by an applied theta-symmetric wall "squeeze"

voltage.

Prior experiments established that this separatrix [1,2]

1) enables and damps the "Trapped Particle Diocotron Mode";

2) damps m! > 0 kz > 0 plasma modes; and

3) adds a new dissipative term in resonant 3-wave couplings.

When external trapping asymmetries such as magnetic tilt are added, the separatrix

4) damps m! > 0 kz = 0 diocotron modes;

5) damps m! = 0 kz > 0 plasma modes; and

6) causes bulk plasma expansion and loss.

Initial theory work by Hilsabeck and O'Neil [3] gave semi-quantitative agreement for

TPDM damping, but theory scalings for all asymmetry-induced effects disagreed with

experiments. For example, Dubin's recent theory and simulation overview of

asymmetry-induced transport with a symmetric trapping separatrix [4] predicts

magnetic scalings differing from experiments (new, this workshop).

The key insight in recent theory work by Tsidulko is that a weak quadrupole (or

higher multipole) perturbation on the (nominally theta-symmetric) separatrix gives

surprisingly large effects. Recent experiments adding such a quadrupole perturbation

show the effect clearly, including a signature cos2(!) dependence on quadrupole angle

relative to tilt angle.

At present, the experimental scalings for all 6 effects are clean and unambiguous, at

least in the limited regimes accessible to room-temperature electron plasmas; but the

theory calculations are difficult. However, it appears that all experimental results are

beginning to fit into a consistent theory framework.



[1] A.A. Kabantsev, and C.F. Driscoll, Phys. Rev. Lett. 97, 095001 (2006).

[2] A.A. Kabantsev et al., Phys. Plas. 10, 1628 (2003).

[3] T.J. Hilsabeck and T.M. O'Neil, Phys. Plasmas 10, 3492 (2003).

[4] D.H.E. Dubin, Phys. Plasmas (to be published, 2008).

15

Turbulent cascade in vortex dynamics of magnetized pure electron

plasmas

Y. Kawai, Y. Kiwamoto, Y. Soga and J. Aoki

Graduate school of Human and Environmental Studies, Kyoto University,Yoshida

Nihonmatsu-cho, Sakyo-ku, Kyoto 606-8501, Japan

Elementary processes of the free-decaying two-dimensional (2D) turbulence are

examined experimentally by extensive analyses of fine-scale structures in the density

of a magnetized pure electron plasma [1]. The observed vortex dynamics start with a

spontaneous formation of vortex patches via a non-linear stage of the diocotron

instability of a ring-shaped initial density distribution [2], and, through successive

mergers between the vortex patches, relax to a stationary state with a single-peaked

distribution (Fig. 1 (top)). In this relaxation process accompanied by the generation of

filamentary fine structures, over a wide range of the wave-number ( k ) space with

k > kinj , the energy spectrum E(k) spreads upward to form a tail that fits to the

power-law k!" with ! ranging from 5.2 to 3.2, where kinj corresponds to the size of

the first-generated patches (Fig. 1 (bottom)). The spectral dynamics of the energy and

enstrophy are examined in terms of the transfer rate in k space on the basis of the

time-resolved spectra. The characteristic features are that the energy is transferred to

larger scales below kinj and that the enstrophy cascades toward smaller scales at a

constant rate in the fine length-scales k > kinj . These spectral dynamics in the k

space are qualitatively consistent with the theoretical description of the 2D turbulence

[3]. However, the observed discrepancies include that the tail of the energy spectrum

is steeper than the theoretical prediction of k!3 and the enstrophy transfer rate is

almost zero around k ! kinj , which indicates the inhibition of the cascade process by

the contribution of the long-persisting coherent vortices [4].

FIG.1: Images of the time evolution of the observed density distribution (top) and

corresponding energy spectra (bottom).

[1] Y. Kawai, et al., Phys. Rev. E 75, 066404 (2007).

[2] A. J. Peurrung and J. Fa jans, Phys. Fluids A 5, 493 (1993).

[3] U. Frisch, TURBULENCE (Cambridge University Press, Cambridge, UK, 1995),

p.241.

[4] P. Santangelo, et al., Phys. Fluids A 1, 1027 (1989).

16

Overview of Intense Beam Simulation Experiments Performed Using the

Paul Trap Simulator Experiment (PTSX)†

E. P. Gilson1, M. Chung

1, R. C. Davidson

1, M. Dorf

1, P. C. Efthimion

1, A. B. Godbehere

2

R. Majeski1

1Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA

2Cornell University, Ithaca, New York, USA

The Paul Trap Simulator Experiment (PTSX) is a compact laboratory linear Paul trap that

simulates the transverse dynamics of a charged-particle bunch coasting through a magnetic

alternating-gradient (AG) transport system. The transverse dynamics of particles in the AG

system in the beam’s frame-of-reference and those of particles in PTSX are described by

similar sets of equations, including all nonlinear space-charge effects. The PTSX voltage

waveform amplitude and frequency correspond to the AG transport system magnet strength

and spacing. Results are presented from experiments in which the lattice period and lattice

field strength are changed over the course of the experiment in order to transversely

compress a beam with an initial normalized intensity s = !p2/2!q

2 ~ 0.2. Both

instantaneous and smooth changes are considered, with an emphasis on determining the

conditions that minimize the emittance growth, and generally, the number of halo particles

produced after the beam compression. Experimental results demonstrating mismatch-

induced beam oscillations and halo particle production are presented. Initial experimental

results are presented in which the collective transverse symmetric mode (m = 0) and

quadrupole mode (m = 2) have been observed in pure-barium-ion plasmas in PTSX for the

purpose of identifying collective modes whose signature will serve as a robust diagnostic

for key properties of the beam, such as line density and transverse emittance. KV-

equivalent envelope equation solutions and the results of PIC simulations performed with

the WARP code agree well with the experimental data.

† Research supported by the U.S. Department of Energy.

17

Brightness and Phase Space Constraints in Free-Electron Lasers

Jonathan S. Wurtele1,2

, M. Gullans3, G. Penn

2, M. Venturini

2, A. A. Zholents

2, and M.

Zolotorev2

1Department of Physics, University of California at Berkeley, Berkeley, CA 94720

2Center for Beam Physics, Lawrence Berkeley National Laboratory Berkeley, CA

94720 3Department of Physics, Harvard University, Cambridge, MA 02138

Free-electron lasers (FELs) are being proposed, and built, as coherent X-ray sources

for a wide variety of scientific applications. They are envisioned as replacing and

augmenting existing synchrotron light facilities. A fundamental requirement for X-ray

FELs is a high brightness (high current and small phase space volume) electron

bunch. The six-dimensional beam brightness is an invariant under Liouvillian flow;

therefore, all non-dissipative manipulations of the phase space (performed, for

example, in order to optimize FEL performance) cannot decrease this brightness. A

new scaling of the FEL equations using the six-dimensional beam brightness will be

presented. This approach leads to a three-dimensional small signal FEL gain length

that scales linearly with current, in contrast to the one-third power current-scaling that

is found by the one-dimensional FEL theory. The brightness-scaled formalism is the

natural one to use to evaluate an array of new ideas for enhancing FEL performance.

We present examples that include beam phase space manipulations, such as localized

bunch compression and longitudinal-transverse phase space exchanges and

correlations. Limits imposed on realizable brightness by both collective instabilities

upstream of the FEL and intrabeam scattering will be discussed.

Work supported by the DOE.

18

Investigations on cooling mechanisms of highly charged ions at

HITRAP

G. Maero1, F. Herfurth, O. Kester

1, H.-J. Kluge

1, S. Koszudowski

1, W. Quint

1, S.

Schwarz2

1GSI, Darmstadt, Germany

2NSCL-MSU, East Lansing, USA

The upcoming facility HITRAP (Highly charged Ion TRAP) at GSI will enable high-

precision atomic-physics investigations of heavy highly-charged ions at extremely

low energies [1]. Species up to U92+

will be produced at the GSI accelerator complex

by stripping of relativistic ions and injected into the Experimental Storage Ring (ESR)

where they are electron-cooled and decelerated to 4 MeV/u. After ejection out of the

ESR and further deceleration in a linear decelerator bunches of 105 ions will be

injected into a Penning trap and cooled to 4 K via electron and resistive cooling. From

this so-called Cooler Trap the cold highly charged ions can be transferred to

experimental set-ups for a large variety of high-accuracy experiments. Simulations

with a Particle-In-Cell (PIC) code have been carried out to study the dynamics of the

ion cloud in the Cooler Trap with focus on resistive cooling in presence of space

charge [2]. For this phenomenon both theoretical and experimental investigations do

not provide extensive and systematic information yet.

[1] F. Herfurth et al., Hyp. Int. 173 (2006) 93.

[2] G. Maero et al., JACoW Proc. of COOL 07, Bad Kreuznach (2008) 130.

19

Measurements of Correlation-Enhanced Collision Rates*

F. Anderegg, C.J. Lee, D. H. E. Dubin, T. M. O’Neil and C. F. Driscoll


Collisional equipartition of parallel and perpendicular kinetic energy is strongly

suppressed at low temperatures in magnetized plasmas, because collisional impact

distances are rarely as small as a cyclotron radius rc. However, theory [1] predicts

that particle correlations reduce this suppression of collisionality, by enhancing the

rare close collisions by about ~e!, where ! " !! ""# is the correlation parameter.

This “Saltpeter correlation enhancement” was first studied for collision-induced

fusion in hot plasmas such as stars [2].

Our preliminary measurements of the perp-to-parallel collision rate !"!! in laser-

cooled Magnesium ion plasmas are consistent with this predicted correlation

enhancement. The plasma temperatures are controlled over the range

! !"#"$ ! ! !"%& , giving measured collision rates !! !""" ! # #!$%&'()!. For slow

collisions, !!! is heated or cooled, and the subsequent relaxation is directly observed.

For rapid collisions, sinusoidal modulation of the plasma length at frequency !!"#

gives maximal heating when !!"# ! !"$$ %&#"'$(, where !!!" is the specific heat. We

effectively eliminate correlation effects by reducing the density from 2 to 0.12

!"# $ %&'(.

Experiments to date clearly show the

expected !"!!#!$"#$ regime at high

temperatures, and the suppression of

!"!! for !" !# !". At low

temperatures and high density, the

measured !"!! is substantially

enhanced over the uncorrelated

prediction (solid curve), and is

consistent with the Saltpeter

enhancement (dashed). At low

density, no enhancement is observed.

At our lowest temperatures, a

“residual” collisionality ! ! "#$%&'(

is observed; this may represent other

interesting physics, or uninteresting

instrumental artifacts.



[1] D.H.E. Dubin, Phys. Rev. Lett. 94, 025002 (2005).

[2] E.E. Salpeter and H.M. Van Horn, Astrophys. J. 155, 183 (1969).

!""

!"#

!"$

!"%& !"%$ !"%# !""

T [eV]

'()*)#

+!#

!!

"#!

")#!"")),-./%!0

rc/ b = 1

20

Excitation of high order diocotron modes in the ELTRAP device

G. Bettega1, F. Cavaliere

1, M. Cavenago

2, B. Paroli

1, R. Pozzoli

1 and M. Romé

1

1 I.N.F.N. Sezione di Milano and Dipartimento di Fisica,

Università degli Studi di Milano, Via Celoria 16, Milano, I-20133, Italy 2I.N.F.N. Laboratori Nazionali di Legnaro,

Viale dell’Università 2, I-35020 Legnaro, Italy

Diocotron modes propagate in a non-neutral plasma trapped in a Malmberg-Penning

trap as density and potential waves having pure azimuthal spatial dependence

exp(il!), and frequency "l depending on the ratio n/B, where n is the particle density

and B the axial confining magnetic field [1]. The mechanism of modes excitation has

been investigated in a pure electron plasma confined in the ELTRAP device [2] by

means of external time-varying electric fields applied to #/2-sectored antennas. An

amplitude modulated quadrupole electric field drives a strong l=2 diocotron mode [3],

while an electrostatic perturbation with a major dipole component, rotating with

respect to the plasma can drive a high amplitude l=3 diocotron [4], if the drive

counter-rotates with respect to the plasma. In both the cases the excitation is resonant,

i.e. maximum deformations of the plasma cross sections have been observed (using a

CCD camera) when the drive frequencies match the natural frequencies of the modes.

First direct experimental measurements of the resistive wave growth of the l=2

diocotron mode have been performed [5]. The results have been interpreted

analytically using the linearized drift-Poisson system in the Fourier (spatial) – Laplace

(temporal) domain and numerically with two-dimensional Particle In Cell simulations.

[1] R. C. Davidson, An Introduction to the Physics of Nonneutral Plasmas (Addison-

Wesley, Redwood City, 1990).

[2] M. Amoretti, G. Bettega, F. Cavaliere, M. Cavenago, F. De Luca, R. Pozzoli, and

M. Romé, Rev. Sci. Instrum. 74, 3991 (2003).

[3] G. Bettega, F. Cavaliere, M. Cavenago, R. Pozzoli, and M. Romé, Phys. Plasmas

14, 102103 (2007).

[4] G. Bettega, F. Cavaliere, B. Paroli, R Pozzoli, and M. Romé, submitted to Phys.

Plasmas.

[5] G. Bettega, F. Cavaliere, B. Paroli, R. Pozzoli, M. Romé and M. Cavenago, Phys.

Plasmas 15, 032102 (2008).

21

Effect of a weakly tilted magnetic field on the equilibrium of

nonneutral plasmas in a Malmberg-Penning trap

M. Romé1 and I. Kotelnikov

2

1 I.N.F.N. Sezione di Milano and Dipartimento di Fisica,

Università degli Studi di Milano, Via Celoria 16, Milano, I-20133, Italy 2 Budker Institute of Nuclear Physics, Lavrentyev Av. 11, Novosibirsk, 630090, Russia

The effect of small asymmetric magnetic field perturbations on the equilibrium of a

nonneutral plasma confined in a Malmberg-Penning trap is analyzed. A constraint

(“condition of current closure”) is derived, that in combination with the Poisson

equation allows to select admissible plasma equilibria in the trap in the presence of a

non-uniform and a non-axisymmetric magnetic field.

The approach is based on previous works on the equilibrium of nonneutral plasmas on

a set of nested toroidal magnetic surfaces [1] and on the equilibrium of quasineutral

plasmas in tandem mirrors [2], and makes use of curvilinear flux coordinates for the

magnetic field [3].

In the particular case of a weakly tilted magnetic field perturbation, two examples of

analytically solvable equilibria are given.

The method can be straightforwardly extended to determine plasma equilibria under

the effect of the magnetic perturbations of higher multipolarity (such as quadrupole or

octupole fields).

[1] T. S. Pedersen and A. H. Boozer, Phys. Rev. Lett. 88, 205002 (2002).

[2] D. D. Ryutov and G. V. Stupakov, in Reviews of Plasma Physics, edited by B. B.

Kadomtsev (Consultants Bureau, New York, 1987), vol. 13, pp. 93-202.

[3] I. Kotelnikov, M. Romé, and A. Kabantsev, Phys. Plasmas 13, 092108 (2006).

22

Drift Motion of Charged Particle

in Electromagnetic Field of Magnetic Pumping

under Cherenkov and Cyclotron Resonance Conditions

K.N. Stepanov, Yu. N. Yeliseyev

Institute of Plasma Physics, National Science Center


The problem on the drift motion of a nonrelativistic charged particle under action of a

helical potential wave of small amplitude [ ]( )exp ( - )m zr i m k z t! "# = # +! ! under

Cherenkov and cyclotron resonance conditions c

n" "$ ( 0, 1, 2,...n = ± ± ) has been

solved in [1-3]. Such a wave can be exited in a plasma cylinder spontaneously as a

result of development of plasma instability or by an external source. This problem is

important for different phenomenon in plasma physics, related with capture of

particles by a wave: nonlinear Landau damping, a nonlinear stage of cyclotron

instability, plasma heating, the anomalous transport of resonant particles in traps.

A particle motion has been described by cylindrical coordinates of a particle Larmor

center R , % , by cylindrical coordinates of a particle on Larmor circle & , ' and by

variables z , z

v . If the wave is absent these coordinates (except for z ) are integrals of

movement. If the wave of small amplitude is present they slowly change. The

equations of particle drift motion valid for arbitrary value of particle Larmor radius &

have been obtained by the averaging method. Three first integrals of the drift motion

have been found. This has allowed to integrate the drift motion equations on time

analytically. For the wave radial function of the form ,( ) ( / )l

m m m lr C J r aµ# =! and

0z

k = the patterns of particle phase trajectories were constructed [3]. The obtained

results have been generalized in [2, 3] on a case when besides the magnetic field the

equilibrium radial electric field, having a potential with a square-law radial

dependence, is present. In the submitted report by the same method the problem is solved on the drift motion

of a charged particle under action of a vortical electromagnetic field, created by a

surface current 0 ( )cos( )z

j j r a k z t! ( "= ) ) , under Cherenkov and cyclotron

resonance conditions. This problem arises in isotope separation by the Ion Cyclotron

Resonance method [4]. The method of solving can be useful for calculation of a

particle transport in traps having a homogeneous magnetic field and small stationary

quadrupole, octupole components of magnetic field [5], affecting resonantly on

particles. The particle drift motion equations are obtained. They are valid at arbitrary Larmor

radius values. The first integrals of drift equations are found. It is interesting, that two

integrals (connecting R , & , z

v ) coincide with integrals of the particle drift motion in

a field of the potential wave with 0m = [1-3].

[1] Yeliseyev Yu.N., Stepanov K.N. Ukrainian Journal of Physics 28, 683-692 (1983)

[2]Yeliseyev Yu.N., Stepanov K.N.Ukrainian Journal of Physics 28,1010-1014 (1983)

[3]Yeliseyev Yu.N. Ph.D. Thesis, Kharkov State University, Kharkov(1984).

[4] Volosov V. I., Demenev V. V. et al. Plasma Phys. Rep. 28, 559-564 (2002).

[5] Fajans J., Madsen N., and Robicheaux R., Phys. Plasmas (2008), in press.

23

Studying of Nonneutral Plasma at Kharkov National University

Yu. N. Yeliseyev2

, A.A. Bizyukov1, D.V. Chibisov

1 , V.I. Farenik

1 ,

Yu.A. Kirochkin1, A.A. Luchaninov

2 , V.S. Mikhailenko

1, M.V. Sosipatrov

2,

K.N. Stepanov1,2

, V.V. Vlasov1, A.V. Zykov

1

1Karazin Kharkov National University, Kharkov, Ukraine

2Institute of Plasma Physics, National Science Center


The studying of nonneutral plasma (in Russian: rotating plasma, plasma in crossed

fields, charged plasma) at Karazin Kharkov National University has been started in

1965 in connection with the problems of RF heating of plasma in fusion devices, of

the ICR-method of separation of isotopes and elements, of plasma technologies.

Plasma, has been created in a self-maintained discharge in a Penning cell and its

modifications under low pressure ( p <!

2·10-4

Torr, 9 3~i e

n n 10 cm!

< , B=100÷1200G,

aV = 500÷2000V, radius of electrodes varied from 1 cm to 14 cm, air, nitrogen,

hydrogen, argon have been used as working gases).

The following results of experimental researches have been obtained.

• The equilibrium plasma parameters (density, potential, longitudinal and

transversal distribution functions (DF) of particles) have been measured [1,2].

• The spectra of unstable natural plasma oscillations have been measured [2]. The

identification of types of natural oscillations has been carried out. The instability,

named Resonant Cyclotron Instability, having frequencies ci

" "# and even

azimuth wave numbers, has been discovered [1].

• The nonlinear parametric interaction of unstable oscillations has been investigated

[2]. The satellites of unstable frequencies have been revealed. The influence of

external oscillations on diocotron plasma oscillations has been investigated.

• The influence of plasma oscillations on particles has been investigated [2]. It has

been found out the reorganization of longitudinal DFs, the broadening of ion DF

over the azimuth moments.

• The phenomenon of energy and space separation of ions of different sorts under

excited Resonant Cyclotron Instability has been discovered [3].

The following results of theoretical researches have been obtained.

• The equilibrium DF of ions born in the crossed fields at rest, have been

determined [4]. The spectra of fluctuations of rotating plasma have been found

under local, and nonlocal [4, 5] considerations.

• The parametric instabilities in the range of lower hybrid and of ion cyclotron

frequencies in plasma with a transverse current have been considered [6]. The

growth rates of these instabilities and estimations of turbulence levels have been

found. These phenomena have been simulated by the method of macroparticles.

[1] A.M. Rozhkov, K.N. Stepanov, V.A. Suprunenko et al.,JETP Lett. 10, 113 (1969).

[2] V.V. Vlasov, V.I. Panchenko, A.M. Rozhkov K.N. Stepanov, V.I. Farenik. Journal

of Technical Physics, 45, 986 (1975). In Russian.

[3] V.V. Vlasov, I.I. Zalubovskij, Yu.A. Kirochkin et al., JETP Lett. 27, 264 (1978).

[4] Yu. N. Yeliseyev, in Non-Neutral Plasma Physics VI, edited by M. Drewsen,

U. Uggerhoj, H. Knudsen (AIP, New York, 2006), 862, 108-115.

[5] D.V. Chibisov, V.S. Mikhailenko, K.N. Stepanov. Plasma Phys. Contr. Fusion, 34,

95 (1992).

[6] A.B. Kitsenko, K.N. Stepanov, in Problemy teorii plasmy: Proc.of the II Intern.

Conf. on Plasma Phys.,Kiev,1976,320-329; V.L. Sizonenko, ibid.,188-195.In Russian.

24

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P*Q!"#![%.1C.8+!L#!\%59.%C.8+!Y#!V5%8.(]%+!^#!,#!V&8GC<+!&89!^#!?#!,E4)FF.%+!?4/C#!:.D#!

Y.<<#!:;+!2T_T!>*``TB#!

P2Q!:#!\Aa'.A+!L#!-&==A.%+!R#b@)8<+!&89!V#R&A<4.%+!?4/C#!:.D#!$!<=+!TMT!>*`T`B#!

25

Spectroscopy of ground state 9Be

+ ions in a 4.5 T Penning trap

N. Shiga1,2

, W. M. Itano1, J. J. Bollinger

1

1NIST, Boulder, CO 80305

2present address: NICT, 4-2-1 Nukui-Kitamachi, Koganei, Tokyo, Japan

We discuss recent measurements of ground-state hyperfine transitions on a few

thousand 9Be

+ ions stored in a 4.5 T Penning trap. At 4.5 T, the ground 2

2S1/2 state

transitions consist of electron spin-flip transitions at ~124 GHz and nuclear spin-flip

transitions at ~300 MHz. By measuring combinations of these transitions we obtained

a measurement of the ground-state hyperfine constant A = -625 008 837.370(10) Hz

at 4.5 T magnetic field [1]. By comparing this value with measurements of A at much

lower magnetic field, we measure a 0.33 Hz diamagnetic correction to A at 4.5 T, in

agreement with theory.

We also summarize our progress towards making entangled internal states of planar

arrays of a few hundred ions. Our qubit (i.e. two-level system) is the 124 GHz

electron spin-flip transition in the 9Be

+ ground state. We plan to use an engineered

spin-squeezing interaction to generate entanglement [2]. Part of the entangling

protocol involves coherent rotations of the qubits, and towards this end we have

characterized the phase and amplitude stability of our 124 GHz microwave source.

With approximately 3 mW of 124 GHz microwave radiation focussed on the ions, we

obtain !-pulse times of approximately 100 "s, and high contrast Rabi oscillations are

observed out to tens of milliseconds (see figure below). The single !-pulse infidelity

due to microwave amplitude instability is less than 10-4

. We observe spin echo

coherence times of 2 ms, which should be sufficient to generate squeezed spin states.

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

Microwave time [ms]

No

rmal

ized

cou

nt

0.0 0.1 0.2 0.3 0.4

0.0

0.2

0.4

0.6

0.8

1.0

25.0 25.1 25.2 25.3 25.4

0.0

0.2

0.4

0.6

0.8

1.0

Rabi flopping obtained on the 124 GHz quibit transition

[1] N. Shiga, et al., in preparation.

[2] D. Leibfried, et al., Nature 438, 639 (2005).

26

Solitary Rarefaction Wave

in Three-Dimensional Complex Plasma

R. Heidemanna , S. Zhdanov

a, R. Sütterlin

a , H. Thomas

a and G. Morfill

a

a Max-Planck-Institut für extraterrestrische Physik

Giessenbachstraße 85748 Garching

Abstract. Observation of a solitary rarefaction wave in a three dimensional complex

plasma is presented. The experiments are performed in a capacitively coupled,

symmetrically driven RF discharge. The discharge chamber is a modified version of the

PK3plus setup installed on board the ISS. A gas temperature gradient of 400K/m is applied

to compensate gravity and to levitate the particles in the bulk plasma. The particle cloud is

formed by monodisperse MF particles with a diameter of 3.42±0.06 !m. The wave is

exited by a short voltage pulse applied to the electrodes of the RF discharge chamber. We

observed a pulse-like wave propagating with an average velocity of 1.14±0.02 cm/s.

Particle dynamics is discussed in detail.

FIGURE 1. Profile of the solitary rarefaction wave in Neon at 24.1Pa

Keywords: solitary rarefaction wave, wave excitation

PACS: 52.27.Lw

27

Structural properties of binary colloidal systems confined in quasi-one-

dimensional channel

K. Nelissen

1, W. Yang

2, M. Kong

3, and F.M. Peeters

1

1Departement of physics, University of Antwerp, B-2020 Antwerpen, Belgium

2Key Laboratory of Materials Physics, Chinese Academy of Science, 230031 Hefei, China

3Institute of Plasma Physics, Chinese academy of Science, 230031 Hefei, China

The structural properties of a binary colloidal quasi-one-dimensional system confined in

a narrow channel are investigated through Monte Carlo simulations. Two species of

particles with different magnetic moment interact through repulsive dipole-dipole force

are confined in a quasi-one-dimensional channel. The impart of three decisive parameters

(total number of particles, magnetic moment ratio and fraction between the two species)

on the transition from liquid-like structures to crystal-like structures are investigated.

Consequently, a general phase diagram as function of three decisive parameters is

obtained. Additional several new properties were found in contrast with other binary and

monodisperse quasi-one-dimensional systems.

28

Dissipation in a 2D classical cluster

K. Nelissen

1, B. Partoens

1, C. Van den Broeck

2, and F.M. Peeters

1

1Departement of physics, University of Antwerp, B-2020 Antwerpen, Belgium

2Departement of physics, University of Hasselt, B-3590 Diepenbeek, Belgium

In Ref [1] one showed through a refinement of the work theorem, that the average

dissipation disW , upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in

a transition between two canonical equilibrium states, is exactly given by:

!"#$" ));(~/);(ln();( tttdTkFWW Bdis %&%&%%& ,

where T is the temperature, Bk is the Boltzmann constant, % is an external control

parameter, F# is the free energy difference between the two equilibrium states, W is the

delivered work, and & and &~ are the phase-space density of the system measured at the

same intermediate but otherwise arbitrary point in time t , for the forward and backward

process respectively. The goal of this work is to find an estimate p for the phase-space

density & by coarse graining. Because p is an estimated quantity the above equality changes

to the inequality:

!'#$ ));(~/);(ln();( tptptpdTkFW B %%%% .

An interesting question is now how this inequality can be verified experimentally. One

possibility is through dusty plasma experiments, were the external control parameter can be

the strength of the parabolic confinement. In this work we will discuss the best coarse

graining strategies which can be applied in an experimental setup. In our simulations we

consider overdamped motion which justifies the use of Brownian dynamics simulations.

We found that a good choice of the coarse graining strategy can improve the estimate of the

average dissipated work significant and that above equation leads to a good estimate of the

average dissipated work even for systems far out of equilibrium.

[1] R. Kawai, J.M.R. Parrondo, and C. Van den Broeck, Phys. Rev. Lett. 98, 080602 (2007)

29

Ion Coulomb Crystals in RF Traps:

Properties and Applications in Cavity QED

Michael Drewsen

QUANTOP - Danish National Research Foundation Center of Quantum Optics,

Department of Physics and Astronomy,

University of Aarhus,

Denmark

When a confined ensemble of charged particles with a single sign of charge is

cooled below a certain critical temperature it forms a very sparse and fragile type of solid,

often referred to as a Coulomb crystal. Recently, we have in a linear RF trap observed

three-dimensional long-range ordered structures in single-species Coulomb crystals

composed of as few as ~1000 40

Ca+ ions. Though this result is unexpected from

molecular dynamics (MD) simulations of the systems ground states, it is found to be in

agreement with MD simulations of metastable ion configurations [1]. We have as well

observed long-range ordered structures in the central 40

Ca+ ion component of

40Ca

+–

44Ca

+

two-species ion Coulomb crystals in a linear Paul trap. The structures here are strikingly

more persistent (lifetimes of ~10 s) and always of one specific type in one particular

orientation. Molecular dynamics simulations strongly indicate that these characteristics

are a consequence of an effective anisotropy in the inter-ion interaction induced by the

radio frequency quadrupole trapping field [2].

Currently, our research on Coulomb crystals is focused on investigations of the

potential of applying such crystals in the study of cavity QED effects as well as cavity

cooling. We have the past year proven it possible to load large ion Coulomb crystals into

a linear RF trap incorporating a high-finesse optical cavity (F >>3200). Even though 3-

mm diameter dielectric cavity mirrors are placed between the trap electrodes and

separated by only 12 mm, it has been possible to produce in situ ion Coulomb crystals

containing more than 105 calcium ions and with lengths of up to several millimeters along

the cavity axis [3]. Most recently, we have also demonstrated that the number of ions

inside the fundamental cavity mode is high enough to reach the so-called strong

collective coupling regime where the exchange of excitations between the cavity field

and the atomic ensemble can take place without decoherence due to spontaneous

emission or cavity photon loss. This feature opens for many fundamental cavity QED

experiments and well as e.g. the construct of quantum memories for light. Finally, how

the coupling between the ion ensemble and the cavity mode can lead to further cooling of

the Coulomb crystal can be investigated..

[1] A. Mortensen, E. Nielsen, T. Matthey, and M. Drewsen, Phys. Rev. Lett. 96,

103001 (2006).

[2] A. Mortensen, E. Nielsen, T. Matthey, M. Drewsen, J. Phys. B40, F223 (2007).

[3] P. Herskind, A. Dantan, M. B. Langkilde-Lauesen, A. Mortensen, J. L. Sorensen,

and M. Drewsen, quant-ph arXiv:0804.4589.

30

Quantum Computation and Quantum Simulation with Coulomb Crystals

Diego Porras and J. Ignacio Cirac

Max-Planck Institute for Quantum Optics, Garching, Germany

Large Coulomb crystals provide us with an interesting system for quantum computation with trapped ions. For example, in Penning traps, a large number of ions (104-106) can be confined by a potential with approximate cylindrical symmetry. If the axial confinement is strong enough, ions arrange themselves in a triangular lattice on a single plane, forming a 2D ion array [1] which is ideally suited for quantum computation. When trying to implement this idea, we face a few problems due to the complicated vibrational level structure of the 2D crystal.

In this work we show how to circunvent these problems by coupling the internal states of the ions (qubits) with the motion in the axial direction (see figure). In particular, we show how it is possible to carry out two-qubit gates between ions with high fidelities by performing a careful analysis of the main sources of decoherence [2].

The results derived here also imply that 2D Coulomb crystals are ideally suited for quantum simulations of condensed matter problems. This may be specially interesting due to the fact that ions are displayed in a triangular structure and, thus, they allow us to study magnetic frustrated systems. The quantum simulation of spin systems is less demanding in experiments, since it does not require single ion gates, and can be implemented by means of lasers that interact simultaneously with all the ions in the crystal.

We also introduce some recent results on the quantum manipulation of 2D arrays of trapped ions in optical lattices, as well as applications of entangled states of ions for the generation of quantum states of light.

[1] W. M. Itano et al., Science 279, 686 (1998).[2] D. Porras and J.I. Cirac, Phys. Rev. Lett. 96, 250501 (2006).

31

PK-3 Plus – Investigation of Complex Plasmas

on the International Space Station

Milenko Rubin-Zuzic1, Hubertus M. Thomas

1, Gregor E. Morfill

1,

Vladimir E. Fortov2, Alexey Ivlev

1, Hermann Rothermel

1, Mierk Schwabe

1,

Vladimir I. Molotkov2, Oleg F.Petrov

2, Andrey I. Lipaev

2

1Max-Planck Institut für extraterrestrische Physik, 85741 Garching, Germany

2RAS- Institute for High Energy Densities, Izhorskaya 13/19, Moscow, 127412, Russia

Complex plasmas are consisting of electrons, ions, neutral gas and in addition

micron-sized particles [1]. Due to their high charge the microparticles interact

strongly among each other and can even form liquid and crystalline systems.

On Earth the corresponding structures are strongly affected by the gravitational force.

For the investigation of the wide phase space of complex plasmas experiments in

microgravity conditions are therefore essential.

PKE-Nefedov, launched in 2001 and operational until 2005, was the first natural

science experiment aboard the ISS for the investigation of complex plasmas in space

[2-3]. It is followed by the successor PK-3 Plus, which has a more sophisticated hard-

and software system.

Extensive dedicated experiments in the PK-3 Plus laboratory were performed by the

Russian cosmonauts V. Tokarev, P. Vinogradov, M. Turin, F. Yurchikhin and Y.

Malenchenko, as well as the German ESA astronaut T. Reiter.

A broad range of parameters was investigated in so-called basic experiments and

many new phenomena related to liquid and crystalline complex plasmas were

discovered [4].

In our presentation we will give an overview of the scientific results gained in the

PK-3 Plus experiments on the International Space Station. Interesting examples are

the experimental discovery of "electrorheological complex plasmas" [5] and the

spontaneous appearance of waves and oscillations in the microparticle component [6].

References:

[1] G. E. Morfill et al., A review of liquid and crystalline plasmas – new physical

states of matter?, Plasma Phys. Control. Fusion 44, B263, 2002

[2] Anatoli P Nefedov, et al., PKE–Nefedov: plasma crystal experiments on the

International Space Station, New Journal of Physics 5, 33.1–33.10, 2003

[3] A. V. Ivlev et al., Coagulation of charged microparticles in neutral gas and charge

induced gel transitions, Phys. Rev. Lett. 89, 195502, 2002

[4] H. M. Thomas et al., Complex plasma laboratory PK-3 Plus on the International

Space Station, New J. Phys. 10 033036, 2008

[5] A.V. Ivlev et al., First observation of electrorheological Plasmas, Phys. Rev. Lett.

100 095003, 2008

[6] M. Schwabe et al., Nonlinear waves externally excited in a complex plasma under

microgravity conditions, New J. Phys. 10 033037, 2008

32

Investigation of space-charge phenomena in gas-filled Penning traps

Sven Sturm1, Klaus Blaum

1,3, Martin Breitenfeldt

4, Pierre Delahaye

2, Alexander Herlert

2,

Lutz Schweikhard4, Fredrik Wenander

2

1 Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany

2 CERN, Geneva, Switzerland

3 Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany

4Ernst-Moritz-Arndt-Universität, 17486 Greifswald, Germany

The centering of ions in Penning traps by quadrupolar excitation in the presence of a buffer gas

has been studied for the case of high charge-densities. The cooling resonance is found to deviate

significantly from the single-particle situation. In particular, the efficiency of the cooling process

is affected as well as the resolving power that can be obtained. The behavior has been studied

experimentally at the preparation trap REXTRAP and the high-precision Penning trap setup

ISOLTRAP both located at the mass separator ISOLDE at CERN. In addition, the phenomenon

has been investigated numerically by a custom-designed simulation tool and, furthermore, a

consistent analytical description has been found. The presentation will include the methods and

results of all three aspects, experimental findings, analytical model and numerical simulations.

33

Barium Ions for Quantum Computation

M. R. Dietrich1, R. Bowler1, N. Kurz1, V. Mirgon1, J. Pirtle1, J. S.Salacka1, G. Shu1, B. B. Blinov1

1Physics Department, University of Washington, Seattle, Washington 98195

We report the initialization and state detection of 137Ba+ hyperfine qubits.We load 137Ba+ into a linear Paul trap by direct photoionization with aXe discharge lamp. The qubit is initialized by optically pumping into themagnetic field insensitive hyperfine ground state (F = 2,mf = 0). Stateselective shelving to the metastable D5/2 state is accomplished by adiabaticrapid passage using a 1762 nm fiber laser stabilized to a high-finesse cavity,a process which is used for high efficiency state detection.

34

Lane Formation in Complex Plasma

R. Sütterlin1, A. Ivlev

1, M. Rubin-Zuzic

1, A. Wysocki

3, H. Löwen

3,

H. M. Thomas1, G. E. Morfill

1, V. E. Fortov

2, H. Rothermel

1, V. I. Molotkov

2,

O. F.Petrov2, A. I. Lipaev

2

1Max-Planck-Institut für extraterrestrische Physik, D-85748 Garching, Germany 2RAS - Institute for High Energy Densities, Izhorskaya 13/19, Moscow, 127412,

Russia

3Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, D-40225

Düsseldorf, Germany

Complex plasmas consist of charged micro particles embedded in ordinary plasma

(electrons, ions and neutral gas). Such systems can serve as suitable model systems

for the examination of e.g. self-organization, atomic or molecular systems, and

transport phenomena at the kinetic level.

Lane Formation is a process of self-organisation: Under certain circumstances, when

two particle ensembles interpenetrate each other – e.g. pedestrians walking in

opposing directions across a pedestrian crossing – individuals do not move

independently, but form lanes or strings.

The inter-penetration of two different complex plasmas is discussed in detail.

Experiments were conducted under microgravity on board the ISS, using the

PK-3 Plus setup. Simulations are used to better understand critical parameters.

In the experiment particles of 9 !m diameter (in Ar at 30 Pa) form a stable complex

plasma cloud with a void in the centre of the chamber. When small particles of 3.2 !m

are injected from the edges they penetrate the cloud of larger particles towards the

void where their trajectories stop. (The picture on the left shows the real experiment,

on the right the corresponding simulation is shown.)

At first single small particles randomly scatter on the outer boundary of the complex

plasma formed by the large particles. Then the small particles collect in streamers or

lanes (cf. [1]), and penetrate through the larger particles. They also create lanes in the

background, which dissolve over time due to Brownian motion.

Similar experiments have been conducted, but with lower density of incident particles

(‘classical tunnelling’, [2]) in which case the structure of the background particles

remains unmodified.

[1] J. Chakrabarti, J. Dzubiella, and H. Löwen, Reentrance effect in the lane formation

of driven colloids, Physical Review E 70, 012401, 2004.

[2] G. E. Morfill, U. Konopka, M. Kretschmer, M. Rubin-Zuzic, H. M. Thomas, S. K.

Zhdanov and V. Tsytovich, The 'classical tunnelling effect' – observations and theory,

New Journal of Physics 8 (7), 2006.

35

Melting processes in anisotropic Coulomb balls

S. W. S. Apolinario and F. M. Peeters

Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020

Antwerpen, Belgium

Dynamical properties of three-dimensional clusters of classical charged particles

trapped in an external potential were studied using molecular dynamics simulation.

We found that an anisotropically confined Wigner crystal of Coulombic interacting

particles exhibit inhomogeneous melting. The region of the system closest to the

center of the cluster has a lower melting temperature than the extremum parts of the

cluster. Moreover, the melting temperature of the cluster depends on the specific

ordered three-dimensional (3D) state [1], i.e. it is larger when the cluster is in the

multiple ring structure arrangement than when it has a non-symmetric configuration.

[1] S. W. S. Apolinario, B. Partoens, and F. M. Peeters, Phys. Rev. B 77, 035321

(2008).

36

Achieving Long Confinement in a Toroidal Electron Plasma

J.P. Marler* and M.R. Stoneking

Lawrence University, Appleton, Wisconsin USA 54912

Trapping non-neutral plasmas in toroidal geometry poses unique challenges and offers

avenues to interesting new physics studies. Experiments that seek to trap non-neutral

plasmas with a toroidal magnetic field must contend with the !B and curvature drifts

by rapidly establishing space charge to generate sufficient poloidal roation. We

observe the m=1 diocotron in a partially toroidal trap[1], and use it as the primary

diagnostic for observing the plasma confinement. The frequency of the m=1 mode,

which is approximately proportional to the trapped charge, decays on a three second

timescale[2]. The confinement time exceeds, by at least an order of magnitude, the

confinement observed in all other toroidal traps for non-neutral plasmas and

approaches the theoretical limit set by magnetic pumping transport[3]. Numerical

simulations that include toroidal effects are employed to accurately extract plasma

charge, equilibrium position and m=1 mode amplitude from the experimental data.

Future work will include attempts to withdraw the electron source in order to study

confinement in a full torus.

Figure 1. Wall probe signal from one electrode for cases where the m=1 mode

was launched at different times (indicated by arrows) relative to initiation of the

trapping phase: a) 0.40 s, b) 1.00 s, and c) 1.80 s. Even after 1.80 s a clear signal

of the plasma is seen.

This work is supported by the National Science Foundation and the U.S. Dept. of

Energy.

*Present Address: University of Aarhus, Denmark

[1] M.R. Stoneking et al, Phys Rev. Lett. 92, 095003 (2004)

[2] J.P. Marler and M. R. Stoneking, Phys. Rev. Lett 100, 155001 (2008)

[3] S.M. Crooks and T.M. O’Neil, Phys. Plasmas 3, 2533 (1996)

37

Recent progress on toroidal non-neutral plasmas

confined on helical magnetic surfaces

H. Himura1, K. Nakamura

1, D. Sugimoto

1, S. Masamune

1, M. Isobe

2, F. Sano

3

1Kyoto Institute of Technology, Department of Electronics, Kyoto 606-8585, Japan

2National Institute for Fusion Science, Gifu 509-5292, Japan

3Kyoto University, Institute of Advanced Energy, Uji 611-0011, Japan

Two topics on toroidal non-neutral plasmas confined on CHS magnetic surfaces and the first

results from the Heliotron-J device are presented.

Firstly, non-constant space potential !s and electron density ne on magnetic surfaces of helical

nonneutral plasmas are observed in CHS experiments [1]. The variation of !s grows with

increasing electron injection energy, implying that thermal effects are important when

considering the force balance along magnetic field lines. These observations confirm the

existence of plasma equilibrium having non-constant !s and ne on magnetic surfaces of helical

nonneutral plasmas predicted by Pedersen and Boozer [2].

Secondly, a numerical work on how the electrons injected from the outside of closed helical

magnetic surfaces (closed B-surfaces) can penetrate deeply in the vacuum magnetic surfaces is

described. In both the CHS and Heliotron-J devices, helical non-neutral plasmas are produced by

electrons injected in the ergodic magnetic region which spreads outside the closed B-surfaces.

Thus, there has been a question how the injected electrons drift across the closed B-surfaces in

order to form the helical non-neutral plasmas. Recently, a numerical calculation including

self-electric potential1 outputs the orbits of injected electrons which extend to the vicinity of the

magnetic axis. The pitch angle of the injected electron is scattered by the self-electric potential in

the ergodic magnetic region, and accordingly, some orbits turn to be those of helically trapped

particles which can drift across the closed B-surfaces along the mod |B| contour curves [3].

Thirdly, as stated above, we report on first results from the Heliotron-J device at Kyoto

University. Like the CHS device, Heliotron-J is one of helical devices, which thus offers a

possibility of investigating unresolved phenomena observed in past CHS non-neutral experiments.

We have just performed the first series of experiments on Heliotron-J. The data show that the

electron injection from the outside of the closed magnetic surfaces is successfully attained and

the non-constant !s and ne seems to be formed also on magnetic surfaces of Heliotron-J

non-neutral plasmas [4].

[1] H. Himura et al., Phys. Plasmas 14, 022507 (2007).

[2] T. S. Pedersen and A. H. Boozer, Phys. Rev. Lett. 88, 205002 (2002).

[3] K. Nakamura, H. Himura, M. Isobe et al., `Inward drift of electrons across helical magnetic

surfaces triggered by self-electric potential in ergodic magnetic region’, to be submitted.

[4] H. Himura et al., under preparation for submission.

38

Confinement and transport in the CNT stellarator

Thomas Sunn Pedersen, J. W. Berkery, P. Brenner, M.S. Hahn, Q. R. Marksteiner, B.

Durand de Gevigney, H. Himura*

Columbia University, New York, NY, USA

*Kyoto Institute of Technology, Kyoto, Japan

The Columbia Non-neutral Torus is a stellarator devoted to non-neutral and electron-

positron plasma research. Confinement and transport processes have been studied in

some detail now, and an understanding of these processes has emerged. Transport is

driven in two ways: The presence of internal rods [Kremer et al., PRL 2006], and the

presence of neutrals. Both transport processes are clearly distinguished experimentally,

and a model of the rod driven transport has been developed, yielding very good

agreement with experimental data [Berkery et al., POP 2007]. The neutral driven

transport is faster than originally expected and indicates the presence of unconfined orbits

in CNT. Numerical modeling of the electron orbits in CNT confirms the existence of loss

orbits and shows that a flux surface conforming electrostatic boundary will greatly

improve confinement [Durand de Gevigney et al., this conference]. Such a boundary has

now been installed in CNT, with initial results showing an order of magnitude

improvement in confinement [Brenner et al., this conference].

39

Studies of a Parallel Force Balance Breaking Instability in a Stellarator

Q. R. Marksteiner, T. Sunn Pedersen, J.W. Berkery, M.S. Hahn, J.M. Mendez, B. Durand de Gevigney,

H. Himura, D. Boyle, and M. Shulman

An instability has been observed in non-neutral plasmas confined on magnetic surfaces in the presence

of a finite ion fraction [Phys. Rev. Letters 100, 065002 (2008)]. In the Columbia Non-neutral Torus

(CNT) the instability has a poloidal mode number of m = 1. This does not correspond to a rational

surface, implying that the parallel force balance of the electron fluid is broken. In CNT, there is a large

variation in the magnetic field, and a large fraction (~65%) of the electrons are on trapped orbits. We

present a summary of key experimental observations of the instability, including the dependence on

neutral pressure, magnetic field strength, and ion species. A simple analytical theory which describes

the above mentioned instability in terms of these trapped electrons is also presented. The bulk of the

trapped and untrapped electrons obey parallel force balance and hence are in a Boltzmann distribution.

However, there is a perturbed component of the trapped electrons which depart from this equilibrium.

These electrons exhibit orbits which ExB drift in the perturbed electric field, and interact with the finite

fraction of ions to cause the plasma to go unstable. Results from this theory will be presented and

compared with experimental results.

40

A Multicell Trap for Storage of Large Numbers of Positrons*

J. R. Danielson, T. R. Weber, C. M. Surko


Penning-Malmberg traps have proven useful, and sometimes critical for the

accumulation, storage and manipulation of positron plasmas [1]. Scientific applications of

these plasmas include creating cold, trap-based beams for atomic physics studies and

tailored sources of positrons for the formation of antihydrogen atoms and positronium

molecules (Ps2). Technological applications include forming state-of-the-art positron

beams for materials analysis. Generally, the capacity of such traps is expected to be

limited by the space charge of the plasma which, is proportional to the total particle

number per unit length of the plasma. For example a plasma of 1011

particles, 10 cm in

length, requires a confinement potential of ~ 7 kV. In order to circumvent this limitation,

we proposed a multicell architecture for an antimatter trap, in which multiple traps are

arranged in parallel and series (shielded from one another by electrodes) in a common

solenoidal magnet and vacuum system [2].

We describe here techniques that will aid in the practical implementation of this multicell

trap [2, 3]. It is designed to increase positron storage by orders of magnitude (e.g., to

particle numbers N > 1012

). The experiments are done using test electron plasmas with

the required cooling provided by cyclotron radiation in a 5 tesla magnetic field. A

technique is described to move plasmas rapidly across the magnetic field and dump them

at specific radial and azimuthal locations (i.e., to fill off-axis cells). Techniques are

demonstrated to operate two in-line plasma cells simultaneously and the use of 1 kV

confinement potentials to trap in excess of 3x1010

particles. These experiments establish

the capability to create, confine, and manipulate plasmas with the parameters required for

a multicell trap, namely N > 1010

in a single cell with temperatures < 0.2 eV, plasma

lengths ~ 10 cm, and radii ~ 0.2 cm. The design of a new electrode structure to test the

confinement of plasmas in off-axis cells will be described, as well as a further-improved

design of a multicell positron trap for 1012

particles. Potential applications, including

prospects for a portable positron trap (e.g., to replace conventional isotope and

accelerator-based sources), will be discussed.

* This work is supported by the National Science Foundation, grant

PHY 07-13958.

1.

C. M. Surko and R. G. Greaves, Phys. Plasmas 11, 2333 (2004).

2.

C. M. Surko and R. G. Greaves, Rad. Chem. and Phys. 68, 419 (2003).

3.

J. R. Danielson, T. R. Weber, and C. M. Surko, Phys. Plasmas 13, 123502 (2006).

41

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42

Studies Of Enhanced Confinement In The Columbia Non-Neutral Torus

Paul W. Brenner, Thomas Sunn Pedersen, Michael S. Hahn,John W. Berkery, Remi G. Lefrancois, and Quinn R. Marksteiner

Department of Applied Physics and Applied Mathematics,Columbia University, New York, New York 10027

(Dated: May 6, 2008)

Recently the measured confinement time in the Columbia Non-neutral Torus (CNT) has beenincreased by nearly an order of magnitude to 190 ms. Previously, enhanced transport caused inpart by the mismatch of constant potential and magnetic surfaces limited confinement times to 20ms. A conducting boundary conforming to the last closed magnetic flux surface has been installedto minimize potential variation along magnetic surfaces, provide new methods to influence theplasma, and act as an external diagnostic. A summary of new results with the conducting boundaryinstalled will be presented, including the dependence of confinement on neutral pressure, magneticfield strength, and the effect of biasing individual sectors of the mesh. Experiments to measureconfinement without internal probes will also be discussed.

43

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44

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45

Pure Electron Equilibrium and Transport Jumps in the Columbia

Non-neutral Torus

Michael Hahn1, Thomas Sunn Pedersen, John W. Berkery, Quinn Marksteiner, and

Paul Brenner

1Columbia University

The Columbia Non-neutral Torus (CNT) is a simple stellarator, which is currently

being used to study electron rich plasmas. At very low neutral pressures these plasmas

are pure electron plasmas. The equilibrium of such plasmas is determined by

electrostatic force balance, which makes the electrostatic boundary conditions

important. One characteristic of the equilibrium is an axial density variation caused

by toroidal differences in the cross sectional geometry. This variation has now been

confirmed experimentally and is in rough agreement with numerical predictions.

Another property of the equilibrium is that if the emitter is placed off the axis the

equilibrium on the inner surfaces is consistent with a global thermal equilibrium.

Recently a conducting boundary conforming to the last closed flux surface was

installed. Experimental studies have been done to characterize the equilibrium with

this new boundary condition. Comparisons of the equilibrium for each boundary

condition will be presented.

For an emitting filament within the plasma the loss rate of electrons from the plasma

is the same as the total emission current in steady state. As parameters that increase

transport are varied abrupt jumps in the emission current occur. These jumps occur at

particular emission currents, and imply discontinuous changes in the confinement

time. They are accompanied by a measurable change in the equilibrium. Using

multiple emitters it has been shown that the jumps occur at the local emission current,

not the total loss rate from the plasma, which implies that the jumps are caused by a

cathode instability.

46

Modeling Wall Probe Signals in a Toroidal Electron Plasma

M.R. Stoneking, Bao Ha†, and J.P. Marler*

Lawrence University, Appleton, Wisconsin USA 54912

Toroidal electron plasmas are confined for several seconds in a new device, the

Lawrence Nonneutral Torus II (LNT II)[1]. Measurements of image charge induced

on sections of a gold plated electrode provide the primary means of studying the

plasma. The frequency of the m=1 diocotron mode determines the total charge in the

plasma while the mode amplitude and character yield information about the absolute

size and shape of the center of mass trajectory as well as the equilibrium major radial

position. We present numerical simulations of the image charge signal for an electron

plasma confined in LNT II, and employ our calculations to extract plasma

characteristics from experimental data. The mean electron density is typically n ~107

cm-3

and decays on a timescale that is of order three seconds. An analysis of the

dynamics and evolution of the electron plasma over this timescale will be presented as

well as plans to measure and model the m=2 diocotron mode. This work is supported

by NSF Grant PHY-0317412.

†Present Address: California Institute of Technology

*Present Address: University of Aarhus, Denmark

[1] J.P. Marler and M. R. Stoneking, Phys. Rev. Lett 100, 155001 (2008)

47

Fluorescence Spectroscopy and Ion Temperature Evolution in

Ultracold Neutral PlasmasJ. A. Castro

1, H. Gao

1 and T. C. Killian

1

1 Department of Physics and Astronomy and Rice Quantum Institute,

Rice University, Houston, TX 77005, USA

Plasma ion temperatures and expansion dynamics are studied through fluorescence

spectroscopy on Ultracold Neutral Plasmas (UNP). Ultracold Neutral Plasmas

(UNP’s) are created by photoionizing laser-cooled atoms; the resulting plasma

expands due to the thermal pressure of the electrons. As the plasma expands, both ion

and electron species undergo adiabatic cooling. Powerful optical diagnostics are

available to study these systems where the initial density profiles, energies, and

ionization states are accurately known and controllable. Spatially-resolved

fluorescence imaging of Ultracold Neutral Plasmas (UNP) produces a spectrum that is

Doppler-broadened due to the thermal ion velocity and shifted due to the ion

expansion velocity. Furthermore, sheet excitation of the plasma allows for localized

analysis of the system without density variation. Using this technique, it is shown that

the plasma undergoes an initial heating of the ions. This effect is combined with

adiabatic cooling which dominates at later times in the expansion.

48

King model for electrons in a finite size ultracold plasma

D Vrinceanu1, G S Balaraman2 and L A Collins1

1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 2School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332

A self consistent model for a finite size non-neutral ultracold plasma is obtained by extending a conventional model of globular star cluster. This model describes the dynamics of electrons at quasi-equilibrium trapped within the potential created by a cloud of stationary ions. A random sample of electron positions and velocities can be generated with the statistical properties defined by this model.

49

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50

First Antihydrogen Production within a Penning-Ioffe Trap

G. Gabrielse1 for the ATRAP Collaboration

1Department of Physics, Harvard University, Cambridge, MA 02138, USA

Slow antihydrogen is produced within a Penning trap that is located within a

quadrupole Ioffe trap, the latter intended to ultimately confine extremely cold, gound-

state antihydrogen atoms. Observed antihydrogen atoms in this configuration resolve

a debate about whether positrons and antiprotons can be brought together to form

atoms within the divergent magnetic fields of a quadrupole Ioffe trap. The number of

detected antihydrogen atoms actually increases when a 400 mK Ioffe trap is turned

on.

51

First attempts at antihydrogen trapping in ALPHA

Joel Fajans

Physics Dept, U.C. Berkeley, Berkeley CA 94720 USA

On behalf of the ALPHA collaboration

The ALPHA experiment is designed to trap antihydrogen atoms in a minimum-B

configuration. The antihydrogen is produced by merging plasmas of positrons and

antiprotons in a cryogenic Penning trap. I will describe the design and operation of the

ALPHA apparatus, with emphasis on the plasma parameters and manipulations most

likely to produce trappable antihydrogen, including recent successful attempts to

compress the antiprotons. I will also discuss the first attempts to detect trapped

antihydrogen.

Antiproton Compression Sequence

This work was supported by CNPq, FINEP (Brazil), ISF (Israel), MEXT (Japan),

FNU (Denmark), NSERC, NRC/TRIUMF (Canada), DOE, NSF (USA), EPSRC and

the Leverhulme Trust (UK) and HELEN/ALFA-EC.

52

Attracting Fixed Points and Strong-drive

Compression of Single-Component Plasmas

J.R. Danielson


The rotating wall (RW) technique has proven to be an excellent method to create

high-density, single-component plasmas in Penning-Malmberg traps. It is now useful,

and sometimes critical, for applications such as antihydrogen production and the tailoring

of ion crystals and positron beams. Azimuthally phased rf fields are used to produce a

torque on the plasma, thereby injecting angular momentum and producing radial

compression.

A recently discovered ‘‘strong-drive’’ regime provides new capabilities, including

the ability to produce high-density steady states with plasma rotation frequencies, fE =

nec/B (with n the plasma density), very close to the applied RW frequency [1-3].

Experiments are done with electron plasmas using a 4.8 tesla magnetic field for strong

cyclotron cooling. The protocol for these experiments is such that the two control

parameters of the system, the RW frequency and amplitude, are set to fixed values; then

the system is allowed to evolve freely to a new steady state in which fE approaches

closely the applied RW frequency. This is in contrast to many previous experiments

where either the RW was tuned to a plasma mode or the amplitude was changed slowly

as the system evolves. These results raise a number of questions, including the nature of

the bifurcation and hysteresis that are observed in the transition between low- and high-

density steady states.

Here, we present a model of the transition to the strong drive regime, describing it

as a competition between attracting fixed points of the system [3]. Key ingredients are a

drag torque due to a plasma-mode resonance driven by static trap asymmetries and a RW

drive torque that passes rapidly through zero as the plasma rotation frequency approaches

the RW frequency. A number of tests of the model are described, including perturbation

experiments to confirm the nature of the RW torque and to measure its magnitude near

the high-density fixed point. Open questions for future research, including what limits the

maximum achievable plasma density and a possible thermodynamic model of the

compression process, will be discussed.

This work is done in collaboration with Cliff Surko and Tom O’Neil and is supported by

NSF grant PHY 03-54653.

[1] J. R. Danielson and C. M. Surko, Phys. Rev. Lett. 95, 035001 (2005).

[2] J. R. Danielson and C. M. Surko, Phys. Plasmas 13, 055706 (2006).

[3] J. R. Danielson, C. M. Surko, and T. M. O'Neil, Phys. Rev. Lett. 99, 135005 (2007).

53

Creation of Finely Focused Beams

from Single-component Plasmas

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54

Radial compression of antiproton cloud for production ofultraslow antiproton beams

N. Kuroda a, Y. Nagata a, H.A. Torii a, K. Komaki a, D. Barna b, D. Horvath b,M. Hori c,d, J. Eades d, H. Imao e, A. Mohri e, M. Shibata e, and Y. Yamazaki a,e

aInstitute of Physics, University of Tokyo, Komaba, Tokyo 153-8902, JapanbKFKI, H-1121 Budapest, Hungary

cMax-Planck-Institute fur Quantenoptik, D-85748 Garching, GermanydDepartment of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan

eRIKEN, Saitama 351-0198, Japan

Cooling and manipulation of a large number of antiprotons held in an electro-magnetictrap are key techniques for the synthesizing antihydrogen atoms and antiprotonic atoms [1].We, MUSASHI sub-group in ASACUSA collaboration, achieved accumulation and coolingof antiprotons with at least 50 times higher efficiency than has been achieved by conven-tional methods [2]. Extracting these antiprotons from the trap and transporting themefficiently in the form of a beam is the next step not only towards synthesizing antihydro-gen atoms for use in CPT symmetry test, but also for studying atomic collision dynamics.Since charged particles tend to follow magnetic field lines, a cloud of antiprotons shouldhave a small radius in the trap for better focusing of extracted beams.We report the radial compression of antiprotons (5 × 105) under ultrahigh vacuum con-ditions (< 10−11 Torr) by applying a rotating electric field. Compression without anyresonant structures like strong drive compression [3] was achieved without electrons ascoolant [4]. Recently compression together with electrons was also tried reported byALPHA collaboration [5].Also our running and planned experiments with such produced ultraslow antiproton beamsat CERN will be discussed, which including atomic collision experiments and antiprotonconfinement in a cusp trap designed for antihydrogen synthesis.

References[1] Y. Yamazaki, Nucl. Instrum. Methods B154 (1999) 174.[2] N. Kuroda et al., Phys. Rev. Lett. 94 (2005) 023401.[3] J. Danielson and C. Surko, Phys. Rev. Lett. 94 (2005) 035001.[4] N. Kuroda et al., Phys. Rev. Lett. to be published.[5] G. B. Andresen et al., Phys. Rev. Lett. to be published.

55

Electrodynamics of neutron star magnetosphere: an example of

non-neutral plasma in astrophysics ?

Jérôme Pétri1

1Centre d’étude des Environnements Terrestre et Planétaires10-12, avenue de l’Europe78140 Vélizy, FRANCE

Although discovered forty years ago, pulsars still rank amongst the most fas-cinating astrophysical objects in the universe. They are believed to be stronglymagnetised rotating neutron stars. However, relatively little progress has beenmade in understanding the fundamental physical mechanisms at work. A globalself-consistent picture of the close surrounding of the star, responsible for theemission of electromagnetic waves and the energy loss due to interaction with theambient medium, has not yet been proposed. Nevertheless, some attempts toconstruct charge separated magnetospheres have been made, [1,2,3].

We give a brief review on the theory of pulsar magnetosphere as well as on somerecent developments. We present a self-consistent model of the magnetosphere ofinactive, charged, aligned rotator pulsars, [4]. The only free parameter is the totalcharge of the system. This “electrosphere” (i.e. the part of the magnetospherefilled with a non-neutral plasma) is to some extent stable to vacuum breakdownby electron-positron pair production. However, it is shown to be unstable to theso-called “diocotron” [5] and “magnetron” [6] instabilities. The evolution of thediocotron instability on a long time-scale is studied in a fully non-linear descrip-tion by means of numerical simulations. For multi-mode excitation, the averagemacroscopic response of the system can be described by a quasi-linear model. Inthe presence of an external source feeding the disk with positive charges, repre-senting the effect of pair creation activity in the gaps, this instability may giverise to an efficient diffusion of charged particles across the magnetic field lines, [5].This phenomenon is a key point to understand pulsars physics.

[1] Krause-Polstorff and Michel, MNRAS, 1985, 213, 43.[2] Thielheim, Wolfsteller, ApJ, 1994, 431, 718.[3] Smith, Michel and Thacker, MNRAS, 2001, 322, 209.[4] Pétri, Heyvaerts and Bonazzola, A&A, 2002, 384, 414.[5] Pétri, Heyvaerts and Bonazzola, A&A, 2002, 387, 520.[6] Pétri, A&A, 2008, 478, 31.

56

Supercomputer modeling of ion cloud motion in mass spectrometers

Eugene Nikolaev1; Ivan Boldin

2; Ron M.A. Heeren

3; Alexander Pozdneev

4;

Alexander Popov4; Pavel Ryumin

1; Gleb Vladimirov

2; Dmitriy Avtonomov

1

1The Institute for Energy Problems of Chemical Phys, Moscow,Russia;

2The Institute of Biochem. Phys. Russian Acad.Sc., Moscow, Russia;

3FOM Inst. Atomic/molecular Physics, Amsterdam, Netherlands;

4Moscow State Uiversity, Dptm. of comp. math., Moscow, Russia;

In a modern high dynamic range mass spectrometer ions are moving in clouds, which

formally should be treated as non neutral plasma objects. Further improvement of

mass accuracy, sensitivity, dynamic range and rate of spectra acquisition demands a

deeper understanding of ion motion dynamics in ion formation, transfer, accumulation

and analysis parts of mass spectrometers. The most challenging problem is taking into

account ion-ion interactions and ion interaction with electrodes. This problem is

getting more pronounced with transition to high dynamic range mass spectrometry,

where number of ions is approaching 10 million and their mutual interaction is getting

comparable to interaction with external fields. The new supercomputer parallel code

was developed to simulate ion motion dynamics in transportation, accumulation and

analysis devices of arbitrary geometry electrodes and arbitrary electric and magnetic

field configurations. This code incorporates the most effective algorithms for electric

field calculations (particle-particle, particle in cell, capacity and surface charge

methods). It enables calculation of fields acting on particles from electrodes and

electric field from ion clouds and ion image charges with today highest accuracy. Ion

dynamic simulation in this code is performed using Boris algorithm, which gives the

highest possible accuracy of trajectory simulations in presence of magnetic fields.

Different approaches currently used for computer simulations of electric fields and ion

motion dynamics in electromagnetic field of different mass spectrometry devices are

analyzed. In these approaches electric field acting on every ion is calculated at every

time step by solving Poisson equation in the whole region of ion motion. To simulate

interaction of ions with image charges capacity matrix method is used. In this method

electrodes are substituted with point capacitors containing charge to compensate for

the potential created by ions on these capacitors making all capacitors on the electrode

equipotential. The total field acting on particular ion in ensemble is calculated as

superposition of the fields from other ions, fields from capacitors and external fields

from electrodes. As an alternative to particle in cell method [1], particle-particle

method was implemented as well. Computer codes were written and implemented

using different parallel supercomputers with shared memory architecture. Comparison

of different codes implementing particle-particle, particle in cell, capacitance and

surface charge methods was made by simulation ion dynamics in ion traps of different

types. Limitations of current supercomputer performance are analyzed and computer

times needed for simulations as a function of the number of ions and the number of

mesh elements were evaluated.

[1] E.N.Nikolaev; R.M.A.Heeren; A.M.Popov; A.V.Pozdneev; K.S.Chingin; Realistic

modeling of ion cloud motion in Fourier transform ion cyclotron resonance cell by use

of a particle-in-cell approach Rapid Commun. Mass Spectrom. 2007; 21,1-20

57

Plasma dynamics and recombination in a high-magnetic-field atom

and plasma trap

G. Raithel, B. Knuffman, C. Hempel, R. Mhaskar, E. Paradis, M. Shah

FOCUS Center, Department of Physics

University of Michigan, Ann Arbor, Michigan

Developments in cooling and trapping of atoms and ions have given birth to the

emerging area of cold, ionized, strongly magnetized matter (magnetized plasmas). We

report on the creation of such plasmas in a particle trap that has the unique capability

to simultaneously laser-cool and trap neutral atoms [1] as well as to confine plasmas

[2] and low-magnetic-field-seeking Rydberg atoms [3] in magnetic fields of about

three Tesla. The atom trap is a high-field Ioffe-Pritchard laser trap, while the plasma

trap is a nested Ioffe-Penning trap that traps electrons and ions in separated wells that

are close to each other. The observed plasma dynamics is characterized by a breath-

ing-mode oscillation of the positive (ionic) plasma component, which feeds back on

the behavior of the negative (electron) component of the plasma [2]. At higher densi-

ties, the observed oscillations become nonlinear. The electron component has been

found to undergo significant cooling. We further report on the recombination of

magnetized plasmas into Rydberg atoms in transient traps and quasi-steady-state

traps. In transient traps (plasma lifetime of order 30 microseconds), large numbers of

recombined Rydberg atoms in high-lying states are observed. In quasi-steady-state

traps, the measured numbers of recombined atoms are much lower, and binding

energies are higher. Results are compared with theory.

Left: Trapping potential (blue curve) along the magnetic-field axis. Electrons are

trapped at the center, while ions are trapped in the wider double-well structure. The

trap can be distorted (red curve) to extract and measure the electron component of the

plasma. Right: Measured electron shake-off signal caused by coupled space-charge

oscillations of the electron and ion components of the trapped plasma. The shake-off

maxima (A-D) occur at the ion breathing-mode frequency. At 450 !s an electron ex-

traction ramp is applied. The extracted electron signal at t > 450 !s is used to deter-

mine the electron temperature.

[1] “Laser cooling and magnetic trapping at several Tesla,” J. R. Guest, J.-H. Choi, E.

Hansis, A. P. Povilus and G. Raithel, Phys. Rev. Lett. 94, 073003 (2005).

[2] “Trapping and evolution dynamics of ultracold two-component plasmas,” J.-H.

Choi, B. Knuffman, X. Zhang, A. P. Povilus, and G. Raithel, Phys. Rev. Lett., in print

(2008).

[3] “Magnetic trapping of long-lived cold Rydberg atoms,” J.-H. Choi, J. R. Guest, A.

P. Povilus, E. Hansis, and G. Raithel, Phys. Rev. Lett. 95, 243001 (2005).

58

Expansion and Equilibration of Ultracold Neutral Plasmas

Thomas C. Killian*

Department of Physics & Astronomy, Rice University; Houston, TX 77005

Ultracold neutral plasmas [1], formed by photoionizing laser-cooled atoms near

the ionization threshold, stretch the boundaries of traditional neutral plasma physics. The

electron temperature in these plasmas is from 1-1000K and the ion temperature is around

1 K. The density can be as high as 1010

cm-3

. Fundamental interest stems from the

possibility of creating strongly-coupled plasmas, but recent experimental and theoretical

work has focused on the equilibration and expansion dynamics.

Using optical absorption [2] and fluorescence imaging, we study expansion

dynamics during the first 50 microseconds after photoionization. Images record the spatial

extent of the plasma, while the Doppler broadened absorption spectrum measures the ion

velocity spectrally. The expansion is driven by the pressure of the electron gas, so the ion

acceleration depends on the electron temperature. Evidence for terminal ion velocity

supports predictions of adiabatic cooling of electrons during expansion [3]. Images

confirm the self-similar nature of a Gaussian density distribution. The expansion is similar

to dynamics of plasmas produced with short-pulse laser irradiation of solid, liquid, foil,

and cluster targets. We will also report results using a new diagnostic that allows us to

follow the evolution of the ion temperature during the expansion.

This work is supported by the National Science Foundation and David and Lucille

Packard Foundation.

* In collaboration with Jose Casto, and Hong Gao.

[1] T. C. Killian, S. Kulin, S. D. Bergeson, L. A. Orozco, C. Orzel, and S. L. Rolston, Phys. Rev.

Lett. 83, 4776 (1999).

[2] C. E. Simien, Y.C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T.

C. Killian, Phys. Rev. Lett. 92, 143001 (2004).

[3] F. Robicheaux and J. D. Hanson, Phys. Plasmas 10, 2217 (2003), T. Pohl, T. Pattard, and J.

M. Rost, Phys. Rev. A 70, 033416 (2004).

59

Low-temperature atom formation in ultracold neutral plasmas

Thomas Pohl

ITAMP, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge MA

02138

The successful creation of ultracold neutral plasmas and cold Rydberg gases has

refocussed attention to the multitude of collisional processes occurring in ionized gases.

Although Rydberg atom formation has been studied for several decades, several

problems, such as diverging recombination rates at high Rydberg states and low

temperatures, remain unsettled.

In this talk, I will discuss how some of these issues can be resolved by

consistently accounting for many-body effects, such as fluctuating electric microfields

and strong correlations between plasma charges. Monte-Carlo simulations suggest

considerable modifications from previously derived and popularly employed rate

formulae. Simulations of the expansion dynamics of ultracold plasmas will be presented,

which permit direct comparisons with experiments, and allow to untangle the various

processes driving the plasma expansion. Our results are shown to successfully describe

current ultracold plasma experiments and to have observable consequences for very

recent measurements. Prospects for the utility of ultracold plasmas to answer such open

questions as, e.g, the stability of high Rydberg states in cold and possibly strongly

coupled plasmas will also be discussed.

60

Ultracold Plasma Expansion and Instabilities

Steven L. Rolston

Joint Quantum Institute, Department of Physics

University of Maryland, College Park, MD

Ultracold plasmas are created by photo-ionization of a sample of laser-cooled atoms,

such that the plasma energy is set by the excess energy of the photon over the

ionization limit, which can be of order a few Kelvin. As the plasmas expand into

vacuum with expansion velocities of order 50 m/s due to electron pressure, the

electron temperature evolves under the competing processes of adiabatic cooling and

recombination-induced heating. Using the Rydberg atoms created during

recombination as a thermometer, we find electron temperatures that fall below 1 K as

the plasma expands in vacuum [1]. The electrons are in an intermediate regime with

Coulomb coupling parameters of ~ 0.1- 0.2, primarily limited by heating due to

recombination collisions. In the presence of a magnetic field aligned with an small

electric field, we observed decreased expansion of the plasma due to radial magnetic

confinement, with expansion velocities reduced by a factor of four in magnetic fields

of 70 Gauss[2]. An ambipolar diffusion model that includes the dynamics of the

evolving plasma is in good agreement with our results. In the presence of a weak (~ 1

G) magnetic field transverse to a weak (~ 10 mV/cm) electric field, we observe

periodic bursts of electrons emitted from the plasma. The frequency of the bursts

scales with E/B, suggesting an instability driven by an E X B drift velocity. The

electrons in the ultracold plasma are magnetized, while the ions remain unmagnetized.

We tentatively identify this instability as being a high field drift instability, similar to

those seen in Hall thrusters plasmas.

[1] R.S. Fletcher, X. L. Zhang, and S. L. Rolston, Phys. Rev. Lett. 99, 145001 (2007).

[2] X. L. Zhang, et al., arXiV 0804.0827.

This work is supported by the National Science Foundation PHY- 0714381.

61

Nonneutral Plasma Physics at Twenty

C. W. Roberson

Office of Naval Research (Ret)

Alexandria, Virginia

[email protected]

The first Nonneutral Plasma Physics Conference was

started in response to the approval of funding for a five-year program by

the Office of Naval Research (1). The National Academy of Sciences

(NAS) was considering the formation of a Plasma Science Committee at

the time and the first conference was held in the NAS facility on the

National Mall. 50 scientists, 9 of whom were from funding agencies,

attended the meeting.

The conference was divided between Nonneutral Plasmas

in traps and beams. Subsequent conferences focused on the enabling

experiments made possible by the first demonstration of a thermal

equilibrium plasma in a Malmberg – Penning trap. Some highlights of the

program over the past twenty years will be discussed.

(1) C. W. Roberson and C. F. Driscoll, Non-Neutral Plasmas

Physics, American Institute of Physics, New York, (1988)

62

9th international work shop on non -neutral plasmas

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