Dynamics of Ions in an Electrostatic Ion Beam Trap

Transcription

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 Charles Coulomb ( ) 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)

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 V 1 V V 1 <V R R Photons can be Trapped in an Optical Resonator L Ions can be Trapped in an Electrical Resonator? E k, q V V>E k /q V

4 Photon Optics Optical resonator Stability condition for a symmetric resonator: L 4 f Symmetric resonator

5 Photon optics - ion optics Optical resonator Particle resonator E k, q V V>E k /q V M Trapping of fast ion beams using electrostatic field L

6 Entrance mirror Field free region L=407 mm Exit mirror Phys. Rev. A, 55, 1577 (1997).

7 Trapping ion beams at kev energies E k Field free region Neutrals Detector (MCP) 1 V 3 4 V 1 V3 V 4 V z V z Why is this trap different from the other traps? No magnetic fields No RF fields No mass limit Large field free region Simple to operate Directionality External ion source Easy beam detection

8 Beam lifetime The lifetime of the beam is given by: τ = 1 σnv n: residual gas density v: beam velocity σ : destruction cross section N(t) = N 0 e ( t ) τ Destruction cross section: Mainly multiple scattering and electron capture (neutralization) from residual gas.

9 Does it really works like an optical resonator? L 4 f Left mirror of the trap V z (varies the focal length) f Step 1: Calculate the focal length as a function of V z

10 Step : Measure the number of stored particles as a function of V z Number of trapped particles as a function of V z.

11 Step 3: Transform the V z scale to a focal length scale L 4 f

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 E k =4. kev Ar + (m=40) W n Pickup electrode E k, m, q W 0 Induced signal on the pickup electrode. T 930 ns (f=340 khz) W n 80 ns 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 W = W + n n 0 T T: Characteristic Dispersion Time

16 How fast does the bunch spread? W n V 1 V 1 W = W + n n 0 T Flatter slope Characteristic dispersion time as a function of potential slope in the mirrors. Steeper slope T=0 No more dispersion??

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

18 Expected W = W + n n 0 T Coherent motion? Dispersion No-dispersion Observation: No time dependence! Shouldn t the Coulomb repulsion spread the particles? What happened to the initial velocity distribution?

19 Injection of a wider bunch:critical (asymptotic) bunch size? W n 1.5 Bunch length (µs) Self-bunching? 0 Asymptotic bunch length X 10 4 Oscillation number n

20 Injection of a wide bunch Asymptotic bunch length n

21 Q 1 : What keeps the charged particles together? Q : Why is self bunching occurring for certain slopes of the potential? Q 3 : 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: V ij = r ij qq i j + const. <v>, v Higher density Stronger interaction W 0 Solve Newton equations of motion Stiff mirrors Soft mirrors interacting non-interacting Bound! non-interacting interacting

23 Trajectory simulation for the real (D) system. Trajectories in the real field of the ion trap Without Coulomb interaction With Repulsive Coulomb interaction E 1 >E

24 What is the real Physics behind this strange behavior? 1D Mean field model: a test ion in a homogeneously charged sphere : V(X) x Nq ρ q L p p Η = NqV(x 1) + qv(x ) + qu(x1 x) m m 1 Sphere-trap Ion-trap interaction interaction Ion-sphere interaction E ρ x ~ r ~ 1/r x Ion-sphere interaction (inside the sphere) 1 U( x) = k x + k ρq 3ε 0 U 0 = interaction strength ( negative k -> repulsive interaction) for x << L, the equations of motion are: x p p/m xqv (X) k x where X is the center of mass coordinate Exact analytic solution also exists.

25 Solving the equations of motion using D mapping mapping matrix M: x p n = M n x p 0 M 1-kT /m = -kt * T/m 1 * Interaction strength T: half-oscillation time m * m/η and η = p P 0 T dt dp 0 Phys. Rev. Lett., 89, 8304 (00) The mapping matrix produces a Poincaré section of the relative motion as it passes through the center of the trap: x Self-bunching: stable elliptic motion in phase space

26 Stability and Confinement conditions for n half-oscillations in the trap: x p n = M n x p 0 p Stability condition in periodic systems: Trace(M) < x k = ρq 3ε 0 0 < kt / m * < 4 For the repulsive Coulomb force: k < 0 Self bunching occurs only for negative effective mass, m* Since m * η = m/η P0 T dt dp 0 < 0 dt dp0 > 0 English: The system is stable (self-bunched) if the fastest particles have the longest oscillation time!

27 Synchronization occurs only if dt/dp>0 dt dp0 > 0? Physics 001 Oscillation period in a 1D potential well: T = Lm 4 p p + S m,p L S= slope dt dp = 4 S Lm p if S < if S > p Lm p Lm,, dt dp dt dp > < 0 0 Weak slope yields to self-bunching!

28 What is the kinematical criterion dt/dp > 0? Oscillation time dt/dv>0 v 1 <v Time Ion velocity slow <v> fast F = c q1q z p=f c t p=f c t The Coulomb Repulsive Force

29 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.

30 Exact solution for any periodic system sin( ωt ) cos( ωt ) cos( ηωt ) Trace( M ) = cos( ωt ) + 4 (1 + η) ωt (1 + η) ( ωt ) Repulsive Attractive where ω k / m Trace(M) < Stable exact condition Trace(M) Unstable exact condition 0 < -kt k η/m ρq = 3ε 0 < 4 Impulse approx. works for repulsive interaction (k < 0)

31 Q 1 : What is the difference between a steep and a shallow slope? Q : What keeps the charged particles together? Q 3 : Nice effect. What can you do with it? High resolution mass spectrometry Example: Time of flight mass spectrometry Target (sample) E k,m,q Detector Time of flight: T = L m E k laser L The time difference between two neighboring masses increases linearly with the time-of-flight distance. T = L 1 8mE k m

32 The Fourier Time of Flight Mass Spectrometer Camera MALDI Ion Source Laser Ion trap MCP detector

33 Lifetime of gold ions in the MS trap Excellent vacuum long lifetime!

34 Fourier Transform of the Pick-up Signal Dispersive mode: dt/dp < 0. Resolution: 1.3 khz, f/f 1/ kev Ar + f

35 Self-bunching mode: dt/dp > 0 t meas =300 ms f/f< <3 Hz f (khz)

36 Application to mass spectrometry: Injection of more than one mass m<m Ek 13 Xe +, 131 Xe + Real mass spectrometry: If two neighboring masses are injected, will they stick together because of the Coulomb repulsion? FFT

37 Even more complicated: Mass spectrum of polyethylene glycol H(C H 4 O) n H ONa + H(C H 4 O) n H OK +

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