Dynamics of Ions in an

1
Dynamics of Ions in an Electrostatic Ion Beam Trap
Daniel Zajfman Dept. of Particle Physics Weizmann
Institute of Science Israel and Max-Planck
Institute for Nuclear Physics Heidelberg, Germany

• Oded Heber
• Henrik Pedersen ( MPI)
• Michael Rappaport
• Adi Diner
• Daniel Strasser
• Yinon Rudich
• Irit Sagi
• Sven Ring
• Yoni Toker
• Peter Witte (MPI)
• Nissan Altstein
• Daniel Savin (NY)

Charles Coulomb (1736-1806)
2
Ion trapping and the Earnshaw theorem No
trapping in DC electric fields
The most common traps The Penning and Paul trap
Penning trap DC electric DC magnetic fields
Paul trap DC RF electric fields
3
A new class of ion trapping devices The
Electrostatic Linear Ion Beam Trap
Physical Principle Photon Optics and Ion Optics
are Equivalent
V1
V2
V1ltV2
Photons can be Trapped in an Optical Resonator
Ek, q
Ions can be Trapped in an Electrical Resonator?
V
V
VgtEk/q
4
Photon Optics
Optical resonator
Stability condition for a symmetric resonator
Symmetric resonator
5
Photon optics - ion optics


Optical resonator
Particle resonator
Ek, q
V
V
VgtEk/q
M
Trapping of fast ion beams using electrostatic
field
L
6
Entrance mirror
L407 mm
Field free region
Exit mirror
Phys. Rev. A, 55, 1577 (1997).
7
Trapping ion beams at keV energies
Detector (MCP)
Field free region
Ek
V1
V1
V2
V2
V3
V3
V4
V4
Vz
Vz

• No magnetic fields
• No RF fields
• No mass limit
• Large field free region
• Simple to operate
• Directionality
• External ion source
• Easy beam detection

Why is this trap different from the other traps?
8
Beam lifetime
The lifetime of the beam is given by
n residual gas density v beam velocity
destruction cross section
Destruction cross section Mainly multiple
scattering and electron capture (neutralization)
from residual gas.
9
Does it really works like an optical resonator?
?
?
Vz (varies the focal length)
Left mirror of the trap
f
Step 1 Calculate the focal length as a function
of Vz
10
Step 2 Measure the number of stored particles as
a function of Vz
Number of trapped particles as a function of Vz.
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Step 3 Transform the Vz scale to a focal length
scale
12
Physics with a Linear Electrostatic Ion Beam Trap

• Cluster dynamics
• Ion beam time dependent laser spectroscopy
• Laser cooling
• Stochastic cooling
• Metastable states
• Radiative cooling
• Electron-ion collisions
• Trapping dynamics

13
Ek4.2 keV Ar (m40)
Pickup electrode
Induced signal on the pickup electrode.
Digital oscilloscope
14
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
15
Time evolution of the bunch width
?T Characteristic Dispersion Time
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How fast does the bunch spread?
Wn
V1
V1
Characteristic dispersion time as a function of
potential slope in the mirrors.
?T0 ? No more dispersion??
17
T15 ms
T5 ms
T1 ms
T30 ms
T50 ms
T90 ms
18
Expected
Coherent motion?
Dispersion
Observation No time dependence!
Shouldnt the Coulomb repulsion spread the
particles? What happened to the initial velocity
distribution?
No-dispersion
19
Injection of a wider bunchCritical (asymptotic)
bunch size?
1.5
Wn
1
Self-bunching?
Bunch length (?s)
0.5
Asymptotic bunch length
0
2
1
3
X 104
0
Oscillation number
n
20
Injection of a wide bunch
Asymptotic bunch length
n
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Q1 What keeps the charged particles
together? Q2 Why is self bunching occurring
for certain slopes of the potential? Q3 Nice
effect. What can you do with it?
There are only two forces working on the
particles The electrostatic field from the
mirrors and the repulsive Coulomb force between
the particles.
-

It is the Repulsive Coulomb forces that keeps the
ions together.
(Charles Coulomb is probably rolling over in his
grave)
22
Simple classical system Trajectory simulation
for a 1D system.
L
Ion-ion interaction
ltvgt, ?v
Higher density Stronger interaction
W0
Solve Newton equations of motion
23
Trajectory simulation for the real (2D) system.
Trajectories in the real field of the ion trap
Without Coulomb interaction
With Repulsive Coulomb interaction
E1gtE2
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What is the real Physics behind this strange
behavior?
1D Mean field model a test ion in a
homogeneously charged sphere
?x
Nq
V(X)
q
?
Sphere-trap interaction
Ion-trap interaction
Ion-sphere interaction
L
Ion-sphere interaction (inside the sphere)
?x
?
interaction strength ( negative k -gt repulsive
interaction)
x
for ?x ltlt L, the equations of motion are
Exact analytic solution also exists.
where X is the center of mass coordinate
25
Solving the equations of motion using 2D mapping
mapping matrix M
T half-oscillation time
and
Interaction strength
Phys. Rev. Lett., 89, 283204 (2002)
The mapping matrix produces a Poincaré section
of the relative motion as it passes through the
center of the trap
Self-bunching stable elliptic motion in phase
space
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Stability and Confinement conditions for n
half-oscillations in the trap
Stability condition in periodic systems
Self bunching occurs only for negative effective
mass, m
For the repulsive Coulomb force k lt 0
English
The system is stable (self-bunched) if the
fastest particles have the longest oscillation
time!
Since
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Synchronization occurs only if dT/dpgt0
Physics 001
Oscillation period in a 1D potential well
m,p
Sslope
L
Weak slope yields to self-bunching!
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What is the kinematical criterion dT/dP gt 0?
dT/dvgt0
Oscillation time
v1ltv2
Time
Ion velocity
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Is dT/dPgt0 (or dT/dEgt0) a valid condition in the
real trap?
Negative mass instability region
dT/dE is calculated on the optical axis of the
trap, by solving the equations of
motion of a single ion in the
realistic potential of the trap.
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Exact solution for any periodic system
Trace(M)lt2 Stable exact condition
Attractive
Trace(M)2 Unstable exact condition
Repulsive
Impulse approx. works for repulsive interaction
(k lt 0)
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Q1 What is the difference between a steep and a
shallow slope? Q2 What keeps the charged
particles together? Q3 Nice effect. What can you
do with it?
High resolution mass spectrometry
Example Time of flight mass spectrometry
Target (sample)
Time of flight
Ek,m,q
Detector
The time difference between two neighboring
masses increases linearly with the time-of-flight
distance.
laser
L
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The Fourier Time of Flight Mass Spectrometer
Camera
MALDI Ion Source
Laser
MCP detector
Ion trap
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Lifetime of gold ions in the MS trap
Excellent vacuum long lifetime!
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Fourier Transform of the Pick-up Signal

.

Dispersive mode dT/dp lt 0




Resolution 1.3 kHz, ?f/f?1/300
4.2 keV Ar
?f
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Self-bunching mode dT/dp gt 0
tmeas300 ms
?f/flt 8.8 10-6
lt3 Hz
f (kHz)
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Application to mass spectrometry Injection of
more than one mass
mltm
Ek
Real mass spectrometry If two neighboring
masses are injected, will they stick together
because of the Coulomb repulsion?
132Xe, 131Xe
37
Even more complicated
Mass spectrum of polyethylene glycol
H(C2H4O)nH2ONa
H(C2H4O)nH2OK
38

• Future outlook
• Complete theoretical model, including critical
  density and bunch size
• Peak coalescence
• Can this really be used as a mass spectrometer?
• Study of mode locking
• Transverse mode measurement
• Stochastic cooling
• Transverse resistive cooling
• Trap geometry
• Atomic and Molecular Physics

Combined Ion trap and Electron Target