Plasma Tools for Antimatter Physics*

Tobin R. Weber Physics Department, University of California San Diego

Acknowledgements: C. M. Surko J. R. Danielson E. A. Jerzewski

*This work supported by NSF grant PHY 07-135958. Antimatter Basics

• All known particles have an antiparticle – Equal mass, but opposite charge (q = -q) – Example: Antiprotons, positrons (antielectrons)

• Created during high energy processes when E > mc2 – Radioactive decay – High energy accelerators

• Annihilates with it’s matter counter part Positron Applications • Positron beams to probe surfaces • Creation of antihydrogen at CERN to test CPT symmetry • Positron atomic physics Future…

• Bose-Einstein condensed positronium •Gamma ray laser • Plasma diagnostics (test particle) Current Limitation: Positron Sources

– Low energy positron sources are weak, I ~ pA

Solution: Positron Trapping

– Collect large numbers of positrons in charge particle traps Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Penning-Malmberg Trap

-Uniform density (n ) rigid rotor (E × B drift) 0 f E ∝ n0

-Confined in state of thermal equilibrium -Infinite confinement times -Thermal equilibrium with walls

(Dubin, Rev. of Mod. Phys. ‘99) High Field Trap 120cm -B = 5 T

-Telec~ 10 Ù 300 K -Screen & Camera -“Rotating Wall”

50cm “Rotating Wall” Compression*

f RW > fE compression

f RW < f E expansion

V = VRW cos[(2πfRW) t + θ]

“Strong Drive” regime

X.-P. Huang , et. al., PRL ‘97. Danielson, et. al., PRL 05; 07; Phys. Pl. ‘06. Trapping Parameters Achieved

• N ~ 1010 • T < 20 meV • n ~ 5 × 1010 cm-3 • τ ~ days High Quality Beams from Trap?

• Most positron applications require high quality beams (narrow, bright, and cold)

• Future applications hinge on beam quality Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Extraction Method

2ρb

VC→ VE

Danielson, et. al., Appl. Phys. Lett., 2007. Weber, et. al., Phys. Plasmas, 2008. Beam Measurements Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Beam Model

2e vz min (r) = − []VE −φo (r) me Beam Model

2e vz min (r) = − []VE −φo (r) me

φ 2e vz min (r) = − []VE − o (r) + Δφ(r) me σ

θ Beam Profileσ Theory 2 ⎡ ⎛ rλ ⎞ eΔφ (r) ⎤ (r) = f d 3vvd dz ≈ exp ⎢− ⎜ ⎟ + ⎥ b ∫ p 0 φ ⎜ 2 ⎟ T vz > vz min (r) ⎢ ⎝ D ⎠ ⎥ ⎣ φ ⎦ eN r 2 Gaussian beam Δ (r) ≈ Δ (0) + b L ρ 2 P b σ

θ Beam Profileσ Theory 2 ⎡ ⎛ rλ ⎞ eΔφ (r) ⎤ (r) = f d 3vvd dz ≈ exp ⎢− ⎜ ⎟ + ⎥ b ∫ p 0 φ ⎜ 2 ⎟ T vz > vz min (r) ⎢ ⎝ D ⎠ ⎥ ⎣ φ ⎦ eN r 2 Gaussian beam Δ (r) ≈ Δ (0) + b L ρ 2 P b

σ 2 ⎡ ⎛ r ⎞ ⎤ Beam profile: b (r) = bo exp⎢− ⎜ ⎟ ⎥ ⎜ ρ ⎟ ρ ⎣⎢ ⎝ b ⎠ ⎦⎥ λ 1/ 2 Beam width: b = 2 D (1+ξ ) ξ ρ e2 N eΔφ(r) b Beam parameter: = b = TLP T 0 Test Predictions

••• Gaussian Fit Beamρ Widths λ 1/ 2 b = 2 D (1+ξ )

T = 1 eV T = 0.2 eV e2 N ξ = b TLP

n = 1x109 cm-3 Beam Number Equation: Nb(VE) N = f d 3vvd 3rv b ∫ p v > v (r) φ z z min φ γ 2e vz min (r) = − []VE − o (r) + Δφ(r) me ρ eN ⎡ ⎛ R ⎞ ⎛ R 2 ⎞ r 2 ⎤ Δ (r) ≈ − b + 2 log⎜ W ⎟ + Γ⎜ ρW ⎟ − ⎢ ⎜ ⎟ ⎜ 2 ⎟ 2 ⎥ LP ⎣ ⎝ b ⎠ ⎝ b ⎠ ρ b ⎦ Beam Number Equation: Nb(VE) N = f d 3vvd 3rv b ∫ p v > v (r) φ z z min φ γ 2e vz min (r) = − []VE − o (r) + Δφ(r) me ρ eN ⎡ ⎛ R ⎞ ⎛ R 2 ⎞ r 2 ⎤ Δ (r) ≈ − b + 2 log⎜ W ⎟ + Γ⎜ ρW ⎟ − ⎢ ⎜ ⎟ ⎜ 2 ⎟ 2 ⎥ LP ⎣ ⎝ b ⎠ ⎝ b ⎠ ρ b ⎦

N b = A(VE , plasma parameters ) Test Predictions

T=1 eV n=1x109 cm-3

Only fitted parameter is φ0(0)

Weber, et. al., Phys. Plasmas, 2009. Energy Distribution Function

− E⊥ /T dN b f (E|| , E ⊥ ) ∝ e dV E VE = E||

NOT a thermal beam (i.e., Non-Maxwellian) Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Energy Spread Trends

ΔEth / T = 3 / 2

Low energy spreads ~ 4 K achievable! Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Narrow Beams

ξ = 0.5

RW Compression Narrow Beams

ξ = 0.5

RW Compression Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Multiple Beams: Plasma Recovery Multiple Beams Results

> 50% of plasma ΔNb 1st, 10th, and 20th < 5% extracted Nb beams with RW on

ξ=0.2 Outline

• High Field positron trap • Beams – Extraction method – Predictions and results • Attractive features – Cold beams – Narrow beams – Multiple beams • Electrostatic beams Electrostatic Beam

• Beam in B=0 region

• Applications include: – Microbeams through electrostatic focus and re- moderation – Atomic physics scattering experiments

• Require extraction from the 5 T field Single particle motion

•For slow extraction, particles stayed “glued” to field lines and maintain adiabatic invariant r E B ⊥ = const . B r B •Fast extraction, particles leave field lines and conserve canonical angular momentum with θ “kick”

Lz = const . = rpθ + qrAθ Slow Extraction

ρ Bi bf = ρ bi B f Slow Extraction

ρ Bi bf = ρ bi B f

ρ bf → ∞

ΔE|| = 3 / 2T as B f → 0 ΔE⊥ = 0 ΔE = 3 / 2T Fast Extraction

ρ bf = ρ bi Fast Extraction

ρ bf = ρ bi

2 2 2 2 ΔE⊥ ∝ B ρ b ΔE|| ∝ B ρ b ΔE = 3 / 2T New Experiment

10 G The Beam Line A First Experiment

ΔE ≈ 0.24 eV Advantages of Trap Based Positron Beams

• High brightness and low emittance – Rotating Wall

– Cyclotron cooling to TW

• Reproducible

• Efficiently use most trapped positrons

• Electrostatic beams Conclusions

• Positrons have many exciting applications but require bright, energy resolved sources • Penning-Malmberg trap has a great potential as a future positron source • Demonstrated ability to confine large numbers, and extract tailored, high quality beams • Electrostatic beam has been demonstrated • Exciting new tools to drive positron research! References: ______

T. R. Weber, J. R. Danielson, and C. M. Surko, Phys. Plasmas 16, 057105 (2009). T. R. Weber, J. R. Danielson, and C. M. Surko, Phys. Plasmas 15, 012106 (2008). J. R. Danielson, T. R. Weber, and C. M. Surko, Appl. Phys. Lett. 90, 081503 (2007).

http://positrons.ucsd.edu