1. electrostatic ion beam trap
Ions in an
electrostatic ion beam trap
4th LEIF meeting Belfast 2003
Oded Heber
Weizmann Institute of Science
Israel
Physics:
Daniel Zajfman
Henrik Pedersen (now at MPI)
Michael Rappaport
Sarah Goldberg
Adi Naaman
Daniel Strasser
Peter Witte (also MPI)
Nissan Altstein
Daniel Savin
Chemistry:
Yinon Rudich
Irit Sagi

2. TALK SUBJECTS INTRODUCTION: ELETROSTATIC LINEAR TRAP AND LAB
DYNAMICS OF ION BUNCHES IN THE TRAP
LONG TIME SYNCRONIZATION MODE
DIFFUSION MODE

3. Photon optics - ion optics
Optical resonator
Particle resonator
Ek, q V V
V>Ek/q L M
Trapping of fast ion beams using electrostatic field

4. Entrance mirror
L=407 mm
Field free region
Exit mirror

5. Trapping ion beams at keV energies
Detector (MCP)
Field free region
Neutrals Ek V1 V1 V2 V2 V3 V3 V4 V4 Vz Vz
Why is this trap different
from the other traps?
Physics with the electrostatic
ion beam trap
No magnetic fields
No RF fields
No mass limit
Large field free region
Simple to operate
Directionality
External ion source
Easy beam detection
Metastable states
Bi-molecules
Clusters
Photon induced processes
Electron collisions
Beam dynamics …

6. Lifetime of the metastable 1S0 state of Xe++
Theory
Garstang: 4.4 ms
Hansen: 4.9 ms
Experiments
Calamai: 4.6  0.3 ms
Walch: 4.5  0.3 ms

7. Photon count rate
1S0
=4.46  0.08 ms
3P1
 =380 nm

8. Beam lifetime: 4.2 keV, Xe++ .
Since the beam lifetime
is much longer than the
1S0 state lifetime, there
are no corrections due to
collisions or quenching.
=310  2 ms.
Theory
Garstang: 4.4 ms
Hansen: 4.9 ms
Experiments
Calamai: 4.6  0.3 ms
Walch: 4.5  0.3 ms
Present: 4.46  ms

9. control room
Linear trap
Laser room
Bent trap
Ion sources
Source control

10. Ek=4.2 keV Ar+ (m=40) Pickup electrode Wn Ek, m, q W0
Induced signal on the
pickup electrode.
2Wn T
280 ns
2930 ns
Ek=4.2 keV
Ar+ (m=40)
(f=340 kHz)

11. Time evolution of the bunch length
The bunch length increases because:
Not all the particles have exactly the
same velocities (v/v5x10-4).
Not all the particles travel exactly
the same path length per oscillation.
The Coulomb repulsion force pushes
the particles apart.
After 1 ms (~350 oscillations)
the packet of ions is as large
as the ion trap

12. Time evolution of the bunch width
ΔT: Dispersion
coefficient

13. Harmonic Oscillator
Linear Trap
Oscillation time:
“Time focusing”,”space focusing”,
“momentum focusing”

14. Is dT/dv>0 a valid condition in the “real” trap?
Characteristic time spread
as a function of voltage
on the last electrode of the trap.
Synch.
Diffusion
dT/dv > 0
Dispersion calculated for the
real potential in the 3D ion trap
K dT/dv
dT/dv < 0
Kinematical condition for motion
synchronization: dT/dv > 0

15. T=1 ms
T=5 ms
T=15 ms
T=30 ms
T=50 ms
T=90 ms

16. “Synchronization motion”
Expected
“Synchronization motion”
Dispersion
Observation:
No time dependence!
Shouldn’t the Coulomb repulsion
have spread the particles?
What happened to the initial
velocity distribution?
No-dispersion

17. E1>E2 Trajectory simulation for the real system.
Trajectories in the real field of the ion trap
Without Coulomb interaction
With Coulomb interaction
E1>E2

18. Fourier Transform of the Pick-up Signal.
Non-synchronizing mode: dT/dv < 0
Resolution: 1.3 kHz, f/f1/300
4.2 keV
Ar+ f

19. Application to mass spectrometry: Injection of more than one massEk
m<m
FFT

20. Is dT/dv>0 a valid condition in the “real” trap?
Characteristic time spread
as a function of voltage
on the last electrode of the trap.
Synch.
Diffusion
dT/dv > 0
Dispersion calculated for the
real potential in the 3D ion trap
K dT/dv
dT/dv < 0
Kinematical condition for motion
synchronization: dT/dv > 0

21. Delta-kick cooling (focusing in velocity space)
S. Chu et al., Opt. Lett. 11, 73 (1986) x p x p γ
Phase space
before kick:
Phase space
after kick:
Condition for delta-kick cooling: A correlation in phase space must exist
Experiments performed on neutral atoms or molecules
F. Crompvoets et al., Phys. Rev. Lett., 89, (2002)
E. Marechal et al., Phys. Rev. A, 59, 4636 (1999)
Proposal for charged particles (weakly interacting particles):
Y. Kishimoto et al., Phys. Rev. E, 55, 5948 (1997)

22. dT/dv<0 !! γ Phase space simulation using 20 ions
with equivalent charges of 5 x 105 ions
dT/dv<0 !! γ
Phase space correlation builds up
very fast because of the strong
Coulomb interaction at the turning
points (trap mirrors)

23. τ: half transition time
Delta-kick cooling on strongly interacting particles: Beating the Coulomb force
Ingredients for delta-kick cooling in the trap:
Dispersive mode: dT/dv<0
Fast build up of phase space correlation
Small bunches
U(t)
Bunch motion U0
-Tp Tp t
Optimum
pulse
Kicker
γ: correlation angle
Ek: beam energy
τ: half transition time
through the cooling
electrodes
β: Geometrical factor
Wave form
generator
Trigger

24. Experiment: 5 x 105 Ar+, Ek= 4.2 keV β ≈ 0.78 Tp=0.5 μs γ ≈ 0.01 μs-1
How is “cooling” observed?
If the velocity spread is
reduced, the bunch size
increase should be slower
Apply cooling pulse
Bunch size without kick
13 eV
Bunch size with δ-kick
10.7 eV ΔW

25. Ion bunch motion in the electrostatic trap can be
Summery:
Ion bunch motion in the electrostatic trap can be
in a synchronization mode when dT/dv>0
Application: high resolution mass spectrometry
When dT/dv<0 the bunch is in an enhanced diffusion mode
Application: delta kick cooling
Ion Motion Synchronization in an Ion-Trap Resonator,
Phys. Rev. Lett., pp , 87 (2001).
Phys. Rev. A., pp , 65 (2002).
Phys. Rev. A, pp , 65 (2002).
Phys. Rev. Lett., pp , 89 (2002)
Delta Kick Cooling
Submitted to Phys. Rev. A