Ions in an electrostatic ion beam trap

Oded HeberWeizmann 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

4th LEIF meeting Belfast 2003

• INTRODUCTION: ELETROSTATIC LINEAR TRAP AND LAB

• DYNAMICS OF ION BUNCHES IN THE TRAP

• LONG TIME SYNCRONIZATION MODE

• DIFFUSION MODE

TALK SUBJECTS

Optical resonator Particle resonator

Trapping of fast ion beams using electrostatic field

Photon optics - ion opticsPhoton optics - ion optics

L

M

V V

Ek, q

V>Ek/q

L=407 mm

Entrance mirror

Exit mirror

Field

fre

e r

eg

ion

V1

V4

V2V3

Vz

V1

V4

V2V3

Vz

Field free region

Trapping ion beams at keV energies

• 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?

Detector (MCP)

Ek

Neutrals

Physics with the electrostatic ion beam trap

• Metastable states• Bi-molecules• Clusters• Photon induced processes• Electron collisions• Beam dynamics• …

Lifetime of the metastable 1S0 state of Xe++

TheoryGarstang: 4.4 msHansen: 4.9 msExperimentsCalamai: 4.6 0.3 msWalch: 4.5 0.3 ms

TheoryGarstang: 4.4 msHansen: 4.9 msExperimentsCalamai: 4.6 0.3 msWalch: 4.5 0.3 ms

Photon count rate

=4.46 0.08 ms 3P1

1S0

=380 nm

Beam lifetime: 4.2 keV, Xe++ .

=310 2 ms.

Since the beam lifetimeis much longer than the1S0 state lifetime, thereare no corrections due to collisions or quenching.

TheoryGarstang: 4.4 msHansen: 4.9 msExperimentsCalamai: 4.6 0.3 msWalch: 4.5 0.3 msPresent: 4.46 0.08 ms

TheoryGarstang: 4.4 msHansen: 4.9 msExperimentsCalamai: 4.6 0.3 msWalch: 4.5 0.3 msPresent: 4.46 0.08 ms

Laser room

Ion sources

Source control

Linear trap

Bent trap

control room

Ek, m, q

W0

Pickup electrode

Wn

Ek=4.2 keV Ar+ (m=40)

T 2Wn

2930 ns

280 ns

(f=340 kHz)

Induced signal on thepickup electrode.

Time evolution of the bunch length

The bunch length increases because:

• Not all the particles have exactly the same velocities (v/v5x10-4).

• 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

2220n ΔTnWW

Time evolution of the bunch width

ΔT: Dispersion coefficient

Harmonic Oscillator

Oscillation time:km2πT

0dvdΤ

0;dΕdΤ

Linear Trap

0dvdT

0dvdT

“Time focusing”,”space focusing ,”“ momentum focusing”

Characteristic time spread as a function of voltage on the last electrode of the trap.

DiffusionSynch.

dT/dv > 0

dT/dv < 0

Dispersion calculated for thereal potential in the 3D ion trap

Is dT/dv>0 a valid conditionin the “real” trap?

Kinematical condition for motionsynchronization: dT/dv > 0

K d

T/d

v

T=15 msT=5 msT=1 ms

T=30 ms T=50 ms T=90 ms

“Synchronization motion”

Expected

Observation:No time dependence!

Shouldn’t the Coulomb repulsionhave spread the particles?What happened to the initialvelocity distribution?

2220n ΔTnWW

Dispersion

No-dispersion

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

.

Resolution: 1.3 kHz, f/f1/300

4.2 keVAr+

f

Non-synchronizing mode: dT/dv < 0

Application to mass spectrometry: Injection of more than one mass

FFT

m<mEk

Characteristic time spread as a function of voltage on the last electrode of the trap.

DiffusionSynch.

dT/dv > 0

dT/dv < 0

Dispersion calculated for thereal potential in the 3D ion trap

Is dT/dv>0 a valid conditionin the “real” trap?

Kinematical condition for motionsynchronization: dT/dv > 0

K d

T/d

v

Delta-kick cooling (focusing in velocity space)S. Chu et al., Opt. Lett. 11, 73 (1986)

Phase space before kick:

x

p

x

p

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)

γ

γ

Phase space simulation using 20 ions with equivalent charges of 5 x 105 ions

Phase space correlation builds upvery fast because of the strongCoulomb interaction at the turningpoints (trap mirrors)

dT/dv<0 !!

Delta-kick cooling on strongly interacting particles: Beating the Coulomb force

Ingredients for delta-kick cooling in the trap:

Wave formgeneratorTrigger

Kicker

Bunch motion

1) Dispersive mode: dT/dv<02) Fast build up of phase space correlation3) Small bunches

t

U(t)

U0

2

p0 T

t1UU(t)

Optimumpulse

-Tp Tp

βτ

TγEU

2pk

0 γ: correlation angleEk: beam energy

τ: half transition time through the cooling electrodesβ: Geometrical factor

If the velocity spread is reduced, the bunch size increase should be slower

Bunch size without kick

Bunch size with δ-kick

Apply cooling pulse

How is “cooling” observed?

ΔW

Experiment:5 x 105 Ar+, Ek= 4.2 keVβ ≈ 0.78Tp=0.5 μsγ ≈ 0.01 μs-1

V 168βτ

TγEU

2pk

0

ΔTdEdT

ΔE1

13 eV

10.7 eV

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