Download Ions in electrostatic beam traps

Ions in an
electrostatic ion beam trap
4th LEIF meeting Belfast 2003
Oded Heber
Weizmann Institute of Science
Israel
Chemistry:
•Yinon Rudich
•Irit Sagi
Physics:
•Daniel Zajfman
•Henrik Pedersen (now at MPI)
•Michael Rappaport
•Sarah Goldberg
•Adi Naaman
•Daniel Strasser
•Peter Witte (also MPI)
•Nissan Altstein
•Daniel Savin
TALK SUBJECTS
• INTRODUCTION: ELETROSTATIC LINEAR
TRAP AND LAB
• DYNAMICS OF ION BUNCHES IN THE TRAP
• LONG TIME SYNCRONIZATION MODE
• DIFFUSION MODE
Photon optics - ion optics
Optical resonator
Particle resonator
Ek, q
V
V>Ek/q
M
Trapping of fast ion beams using electrostatic field
L
V
Field free region
Entrance mirror
Exit mirror
L=407 mm
Trapping ion beams at keV energies
Neutrals
Field free region
Ek
V1
V2
V3
V4
V1
V2
V3
V4
Vz
Why is this trap different
from the other traps?
• No magnetic fields
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No RF fields
No mass limit
Large field free region
Simple to operate
Directionality
External ion source
Easy beam detection
Detector (MCP)
Vz
Physics with the electrostatic
ion beam trap
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Metastable states
Bi-molecules
Clusters
Photon induced processes
Electron collisions
Beam dynamics
…
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
Photon count rate
1S
0
=4.46  0.08 ms
3P
1
 =380 nm
Beam lifetime: 4.2 keV, Xe++ .
Since the beam lifetime
is much longer than the
1S state lifetime, there
0
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  0.08 ms
Linear trap
control room
Laser room
Bent trap
Ion sources
Source control
Pickup electrode
Wn
Ek, m, q
W0
Induced signal on the
pickup electrode.
T
2930 ns
(f=340 kHz)
2Wn
280 ns
Ek=4.2 keV
Ar+ (m=40)
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
Time evolution of the bunch width
Wn  W02  n2ΔT2
ΔT: Dispersion
coefficient
Harmonic Oscillator
Oscillation time: T  2π
Linear Trap
dT
0
dv
m
k
dΤ
dΤ
 0;
0
dΕ
dv
“Time focusing”,”space focusing”,
“momentum focusing”
dT
0
dv
Is dT/dv>0 a valid condition
in the “real” trap?
Synch.
Diffusion
dT/dv > 0
Characteristic time spread
as a function of voltage
on the last electrode of the trap.
K dT/dv
Dispersion calculated for the
real potential in the 3D ion trap
dT/dv < 0
Kinematical condition for motion
synchronization: dT/dv > 0
T=1 ms
T=5 ms
T=15 ms
T=30 ms
T=50 ms
T=90 ms
Expected
Wn  W02  n2ΔT2
“Synchronization motion”
Dispersion
Observation:
No time dependence!
No-dispersion
Shouldn’t the Coulomb repulsion
have spread the particles?
What happened to the initial
velocity distribution?
Trajectory simulation for the real system.
Trajectories in the real field of the ion trap
Without Coulomb interaction
With Coulomb interaction
E1>E2
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
.
Application to mass spectrometry: Injection of more than one mass
Ek
m<m
FFT
Is dT/dv>0 a valid condition
in the “real” trap?
Synch.
Diffusion
dT/dv > 0
Characteristic time spread
as a function of voltage
on the last electrode of the trap.
K dT/dv
Dispersion calculated for the
real potential in the 3D ion trap
dT/dv < 0
Kinematical condition for motion
synchronization: dT/dv > 0
Delta-kick cooling (focusing in velocity space)
S. Chu et al., Opt. Lett. 11, 73 (1986)
p
Phase space
before kick:
p
γ
x
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, 093004 (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)
x
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)
Delta-kick cooling on strongly interacting particles: Beating the Coulomb force
Ingredients for delta-kick cooling in the trap:
1)
2)
3)
Dispersive mode: dT/dv<0
Fast build up of phase space correlation
Small bunches
U(t)
Bunch motion
U0
-Tp
Tp
  2 
t
U(t)  U0 1    
  Tp  


U0 
t
Optimum
pulse
γEk Tp2 γ: correlation angle
βτ
Ek: beam energy
τ: half transition time
through the cooling
electrodes
β: Geometrical factor
Kicker
Trigger
Wave form
generator
Experiment:
5 x 105 Ar+,
Ek= 4.2 keV
β ≈ 0.78
Tp=0.5 μs
γ ≈ 0.01 μs-1
U0 
γEkTp2
βτ
How is “cooling” observed?
If the velocity spread is
reduced, the bunch size
increase should be slower
 168 V
dT
ΔE 
dE
Apply cooling pulse
Bunch size without kick
1
ΔT
13 eV
Bunch size with δ-kick
10.7 eV
ΔW
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. 55001, 87 (2001).
•Phys. Rev. A., pp. 42703, 65 (2002).
•Phys. Rev. A, pp. 42704, 65 (2002).
•Phys. Rev. Lett., pp. 283204, 89 (2002)
Delta Kick Cooling
•Submitted to Phys. Rev. A