Erik P. Gilson Princeton Plasma Physics Laboratory Symposium on Recent Advances in Plasma Physics June 11–12, 2007 In Celebration of Ronald C. Davidson's 40 Years of Plasma Physics Research and Graduate Education *This work is supported by the U.S. Department of Energy. The Paul Trap Simulator Experiment* In collaboration with: Moses Chung, Ronald C. Davidson, Mikhail Dorf, Philip C. Efthimion, Richard Majeski, and Edward A. Startsev

Simulate the nonlinear transverse dynamics of intense beam propagation over large distances through magnetic alternating-gradient transport systems in a compact experiment. PTSX Simulates Nonlinear Beam Dynamics in Magnetic Alternating-Gradient Systems Purpose:

The PTSX Group is Like a Family…

…But Different Than Other NJ Families

Beam mismatch and envelope instabilities Collective wave excitations Chaotic particle dynamics and production of halo particles Mechanisms for emittance growth Effects of distribution function on stability properties Compression techniques Scientific Motivation

N N S S x y z Magnetic Alternating-Gradient Transport Systems z S

2 m 0.4 m 0.2 m PTSX Configuration – A Cylindrical Paul Trap Plasma column length2 mMaximum wall voltage~ 400 V Wall electrode radius10 cmEnd electrode voltage< 150 V Plasma column radius~ 1 cmVoltage oscillation frequency < 100 kHz Cesium ion mass133 amuOperating pressure5x10 -9 Torr Ion source grid voltages< 10 V sinusoidal in this work for a sinusoidal waveform V(t). for a periodic step function waveform V(t) with fill factor . When  = 0.572, they’re equal.

Transverse Dynamics are the Same Including Self-Field Effects Quadrupolar Focusing Self-Forces usual  self (x,y,t) Field EquationsPoisson’s Equation Vlasov Equation

Transverse Dynamics are the Same Including Self-Field Effects Long coasting beams Beam radius << lattice period Motion in beam frame is nonrelativistic Ions in PTSX have the same transverse equations of motion as ions in an alternating-gradient system in the beam frame. If… Then, when in the beam frame, both systems have… Quadrupolar external forces Self-forces governed by a Poisson-like equation Distributions evolve according to nonlinear Vlasov-Maxwell equation

1.25 in Electrodes, Ion Source, and Collector 5 mm Broad flexibility in applying V(t) to electrodes with arbitrary function generator. Increasing source current creates plasmas with intense space- charge. Large dynamic range using sensitive electrometer. Measures average Q(r).

s =  p 2 /2  q 2 = / 0 = 0.9 V 0 max = 235 V f = 75 kHz  v = 49 o At f = 75 kHz, a lifetime of 100 ms corresponds to 7,500 lattice periods. If lattice period is 1 m, the PTSX simulation experiment would correspond to a 7.5 km beamline. PTSX Simulates Equivalent Propagation Distances of 7.5 km for Moderately Intense Beams s =  p 2 /2  q 2

Instantaneous Changes in the Voltage and Frequency Do Not Affect the Transverse Profile When  q is Fixed s = 0.2 kT ~ 0.7 eV N ~ constant  v = 33 o  v = 50 o  v = 75 o V,f up to 1.5X Baseline case V,f down to 0.66X

Mismatch Between Ion Source and Focusing Lattice Creates Halo Particles Text box. Qualitatively similar to C. K. Allen, et al., Phys. Rev. Lett. 89 (2002) on the Los Alamos low-energy demonstration accelerator (LEDA). “Simulation” is a 3D WARP simulation that includes injection from the ion source. s =  p 2 /2  q 2 = 0.6. / 0 = 0.63 V 0 max = 235 V f = 75 kHz  v = 49 o Streaming- mode experiment

WARP Simulations Reveal the Evolution of the Halo Particles in PTSX Oscillations can be seen at both f and  q near z = 0. Downstream, the transverse profile relaxes to a core plus a broad, diffuse halo. s =  p 2 /2  q 2 = 0.6. / 0 = 0.63 V 0 max = 235 V f = 75 kHz  v = 49 o  q 1/f

Adiabatic Amplitude Increases Transversely Compress the Beam R b = 0.79 cm kT = 0.16 eV s = 0.18  = 10% Instantaneous R b = 0.93 cm kT = 0.58 eV s = 0.08  = 140% Adiabatic R b = 0.63 cm kT = 0.26 eV s = 0.10  = 10% s =  p 2 /2  q 2 = 0.20 / 0 = 0.88 V 0 max = 150 V f = 60 kHz  v = 49 o 20%90%  v = 63 o  v = 111 o

Less Than Four Lattice Periods Adiabatically Compress the Beam s =  p 2 /2  q 2 = 0.2. / 0 = 0.88 V 0 max = 150 V f = 60 kHz  v = 49 o  v = 63 o  v = 111 o  v = 81 o

2D WARP Simulations Corroborate Adiabatic Transitions in Only Four Lattice Periods Instantaneous Change. Change Over Four Lattice Periods.

Increasing  q by Adiabatically Decreasing f – the Right Way

Predicted  c Based on  v max =  v stability limit Agrees With Data cc

Barium Ion’s Atomic Structure is Amenable to LIF Barium ions are heavy enough (137 amu) to be confined in the PTSX Barium ions are produced primarily in the ground state (6 2 S 1/2 ), but some in the metastable states (5 2 D 3/2, 5 2 D 5/2 ) Because PTSX does not utilize external magnetic field, there is no Zeeman split Because time average electric field vanishes in the PTSX, there is no first order Stark effect

Schematic Diagram of LIF Diagnostic Setup Custom-made Reentrant Flange (A/R Coated)

PTSX is a compact and flexible laboratory experiment. PTSX has performed experiments on plasmas with normalized intensity s up to 0.2. Confinement times can correspond to up to 7,500 lattice periods. Halo particle production that is seen in streaming-mode experiments is due to the mismatch between the ion source and the transverse focusing lattice. Adiabatic increases in the voltage waveform amplitude can be applied over only four lattice periods when making changes of up to 90%. Instantaneous changes cause significant emittance growth and lead to halo particle production. Adiabatic decreases in frequency, when done properly, can be applied over only four lattice periods as well. PTSX Simulates the Transverse Dynamics of Intense Beam Propagation Over Large Distances Through Magnetic Alternating-Gradient Transport Systems