Transcript ppt 2.1MB - Weizmann Institute of Science

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)
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
A new class of ion trapping devices: The Electrostatic Linear Ion Beam Trap
Physical Principle:
Photon Optics and Ion Optics
are Equivalent
V1
V2
V1<V2
R
R
Photons can be Trapped in an
Optical Resonator
L
Ek, q
Ions can be Trapped in an
Electrical Resonator?
V
V>Ek/q
V
Photon Optics
Optical resonator
Stability condition for a symmetric
resonator:
L
 f 
4
Symmetric
resonator
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
Phys. Rev. A, 55, 1577 (1997).
L=407 mm
Trapping ion beams at keV energies
Neutrals
Field free region
Ek
Detector (MCP)
V1
V2
V3
V4
V1
V2
V3
V4
Vz
Vz
• No magnetic fields
Why is this trap different
from the other traps?
• No RF fields
• No mass limit
• Large field free region
• Simple to operate
• Directionality
• External ion source
• Easy beam detection
Beam lifetime
The lifetime of the beam
is given by:
1

σnv
n: residual gas density
v: beam velocity
 : destruction cross section
N(t)  N0e
 
 t
Destruction cross section:
Mainly multiple scattering
and electron capture
(neutralization) from
residual gas.
Does it really works like an
optical resonator?
L
 f 
4
Left mirror of the trap
Vz (varies the focal length)
f
Step 1: Calculate the focal length as a function of Vz
Step 2: Measure the number of stored particles as a function of Vz
Number of trapped particles as
a function of Vz.
Step 3: Transform the Vz scale to a focal length scale
L
f
4
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
Ek=4.2 keV
Ar+ (m=40)
Wn
Pickup electrode
Ek, m, q
W0
Induced signal
on the pickup
electrode.
T
2930 ns
(f=340 kHz)
2Wn
280 ns
Digital oscilloscope
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: Characteristic Dispersion Time
How fast does the bunch spread?
Wn
V1
Wn  W02  n2ΔT2
V1
Flatter slope
Characteristic dispersion
time as a function of
potential slope in the
mirrors.
Steeper slope
ΔT=0  No more dispersion??
T=1 ms
T=5 ms
T=15 ms
T=30 ms
T=50 ms
T=90 ms
Expected
Wn  W02  n2ΔT2
“Coherent motion?”
Dispersion
Observation:
No time dependence!
No-dispersion
Shouldn’t the Coulomb repulsion
spread the particles?
What happened to the initial
velocity distribution?
Injection of a wider bunch:Critical (asymptotic) bunch size?
1.5
Bunch length (s)
Wn
1
Self-bunching?
0.5
Asymptotic bunch length
0
0
1
2
Oscillation number n
3
X 104
Injection of a “wide” bunch
Asymptotic bunch length
n
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)
Simple classical system: Trajectory simulation for a 1D system.
L
Ion-ion interaction: Vij 
<v>, v
qiqj
rij  const.
Higher density
Stronger interaction
Solve Newton equations of motion
W0
Stiff mirrors
Soft mirrors
“Bound”!
non-interacting
interacting
Trajectory simulation for the real (2D) system.
Trajectories in the real field of the ion trap
Without Coulomb interaction
With Repulsive Coulomb interaction
E1>E2
What is the real Physics behind this “strange” behavior?
1D Mean field model: a test ion in a homogeneously charged “sphere”:
Nq
V(X)
Δx
p12
p22
Η

 NqV(x1 )  qV(x2 )  qU(x1  x2 )
2m1 2m2
q
ρ
Sphere-trap
Ion-trap
interaction
interaction Ion-sphere
interaction
L
ρ
E
Ion-sphere interaction (inside the sphere)
Δx
~r
U(x)  12 k x 2  U0
~ 1/r2
x
ρq
k
3ε0
for Δx << L, the equations of motion are:
where X is the center of mass coordinate
interaction strength
( negative k -> repulsive interaction)
Δx  Δp/m
Δp  ΔxqV(X)  kx
Exact analytic solution
also exists.
Solving the equations of motion using 2D mapping
mapping matrix M:
Δx 
 Δx 
n

  M 

 Δp n
 Δp 0
1 - kT 2/m* T/m* 

M  

kT
1


T: half-oscillation time
m  m/η
*
Interaction strength
and
P0 dT
η
T dP0
Phys. Rev. Lett., 89, 283204 (2002)
p
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
x
Stability and Confinement conditions for n half-oscillations in the trap:
Δx 
 Δx 
n

  M 

 Δp n
 Δp 0
Trace(M)  2
Stability condition
in periodic systems:
ρq
k
3ε0
x
0  kT / m  4
For the repulsive Coulomb force: k < 0
2
*
Self bunching occurs only for
negative effective mass, m*
m*  m/η  0
P dT
Since η  0
T dP0
p
dT
0
dP0
English:
The system is stable (self-bunched)
if the fastest particles have the
longest oscillation time!
dT
0?
dP0
Synchronization occurs only
if dT/dp>0
Physics 001
Oscillation period in a 1D potential well:
 Lm p 
T  4
 
2p
S

dT 4 2Lm
  2
dp S
p
m,p
S=“slope”
L

2p2
dT
if S  Lm ,  dp  0


2
2p
dT
if S 
,
0

Lm
dp
“Weak” slope yields to
self-bunching!
Oscillation time
What is the kinematical criterion dT/dP > 0?
v1<v2
Ion velocity
slow
p=Fc t
<v>
fast
p=Fc t
The Coulomb Repulsive Force
Fc 
q1q2
Δz2
Time
dT/dv>0
Is dT/dP>0 (or dT/dE>0) 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.
Exact solution for any periodic system
cos(T )  cos(T )
sin( T )
4
Trace( M )  cos(T ) 
(1   ) 2 (T ) 2
(1   )T
Attractive
where
  k/m
|Trace(M)|<2
Stable exact condition
|Trace(M)|≥2
Unstable exact condition
Repulsive
0  - kT2η/m  4
k
ρq
3ε 0
Impulse approx. works
for repulsive interaction
(k < 0)
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)
Ek,m,q
Detector
laser
L
Time of flight: T
L
m
2Ek
The time difference between two
neighboring masses increases linearly
with the time-of-flight distance.
ΔT  L
1
Δm
8mEk
The Fourier Time of Flight Mass Spectrometer
Camera
MALDI
Ion Source
Laser
Ion trap
MCP
detector
Lifetime of gold ions in the MS trap
Excellent vacuum – long lifetime!
Fourier Transform of the Pick-up Signal
Dispersive mode: dT/dp < 0
Resolution: 1.3 kHz, f/f1/300
4.2 keV
Ar+
f
.
Self-bunching mode: dT/dp > 0
tmeas=300 ms
Δf/f< 8.8 10-6
f (kHz)
<3 Hz
Application to mass spectrometry: Injection of more than one mass
m<m
Ek
“Real” mass spectrometry: If two neighboring
masses are injected, will they “stick” together
because of the Coulomb repulsion?
132Xe+, 131Xe+
FFT
Even more complicated:
Mass spectrum of polyethylene glycol H(C2H4O)nH2ONa+
H(C2H4O)nH2OK+
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