Lanzhou Summer School 2004

Frontiers in Atomic and Molecular Physics with Charged Particles

Klaus BlaumEuropean Organisation for Nuclear Research, CERN,

Physics Department, 1211 Geneva 23, Switzerland

and

Gesellschaft für Schwerionenforschung, GSI, 64291 Darmstadt, Germany

Email: Klaus.Blaum@CERN.ch or blaumk@uni-mainz.de

http://isoltrap.web.cern.ch/isoltrap

Lecture #0

Atomic Physics with Stored andCooled Ions

Klaus BlaumGesellschaft für Schwerionenforschung, GSI, Darmstadt

and CERN, Physics Department, Geneva, Switzerland

Summer School, Lanzhou, China, 9 – 17 August 2004

0. Lecture: Introduction and Motivation

Content

Atomic Physics with Stored andCooled Ions

Introduction and motivationPrinciple of storing charged particles

012 Cooling techniques for charged particles

Production of HCI and radioactive nuclei3Applications and performance of ion traps4

Test of QED in extreme fields: g-factor56 Weak interaction studies

Atomic masses and Penning trap MS7Future techniques and experiments8

Summary and conclusions9

Atomic physics with stored ions at GSI

ATOMIC PHYSICS WITH HIGHLY

CHARGED IONS OREXOTIC NUCLEI

ATOMICSPECTROSCOPY NUCLEAR

GROUND STATE PROPERTIES

HIGH-PRECISION MASS

SPECTROMETRY

DETECTORTECHNIQUES

COOLING TECHNIQUES

CALIBRATIONTECHNIQUES

STORAGE RING TECHNIQUES

CHARGE BREEDING

TECHNIQUES

ION TRAP TECHNIQUES

The history of ion traps

Hans Dehmelt

Seattle Mainz

SMILETRAPATHENA

g-factor trapCPT REXTRAP

Gernot Graeff

CLUSTER TRAP

NIPNET

HITRAP

ATRAPISOLTRAP

Harvard

RETRAP

SCIENCEFrans Michel

PenningWolfgang

Paul EUROTRAPS

EXOTRAPS

MIT

Operational:

e+ TRAP

LEBIT SHIPTRAP JYFL TRAP WITCHIn setup:

MAFF TRAP TRIUMF TRAP HITRAP KVI TRAPFuture projects:

Lecture #1

Atomic Physics with Stored andCooled Ions

Klaus BlaumGesellschaft für Schwerionenforschung, GSI, Darmstadt

and CERN, Physics Department, Geneva, Switzerland

Summer School, Lanzhou, China, 9 – 17 August 2004

1. Lecture: Principle of storing charged particles

1. Why storing? 2. Trapping devices for charged particles

- radio frequency quadrupole (Paul) traps - Penning traps- storage rings

Why storing?

effective use of rare species

easy manipulation of trapped particles

q/m-separation

extended observation & manipulation time

accumulation & bunching

charge breeding

polarization

increase of luminosity

EFFICIENCYACCURACYSENSITIVITY

Pioneers of trapping and cooling in ion and laser traps

Principle of Penning Traps

Frans Michel Penning

Storage and Cooling

of AntiprotonsNobel Prize 1984J. van der Meer

C. Rubbia

Storage and Cooling of AtomsNobel Prize 1997

S. Chu C. Cohen-Tannoudji W. D. Phillips

Bose-Einstein CondensationNobel Prize 2001

E. Cornell W. Ketterle C. Wieman

Storage and Cooling of IonsNobel Prize 1989

H. Dehmelt W. Paul

Principle of trapping

Radial force Harmonic potential Cooling

electric fields

magnetic fields

light fields

damping of oscillationamplitudes

minimization of trap

imperfections

harmonic oscillation

2 or 3 independent

eigen frequencies

“infinite” storage time

Storage devices

Penning and Paul Trap Storage Ring

B

U

0 0.5 1 cm

particles at nearly rest in space relativistic particles

∗ ion cooling ∗ “infinite“ storage time ∗ single-ion sensitivity ∗ high accuracy ∗ mass spectrometric capabilities

Storage of charged particles

required: potential minimum in 3 dimensionsdesired: harmonic force in direction of trap center

→

→ harmonic oscillations

F ~ - r

⇒⇒222 CzByAx ++=φF = -e∇φ ~ - r

in addition: ∆φ = 0 (Laplace equation)z

simplification: rotational symmetry (z-axis)y

x

Storage of charged particles in an ion trap

⇒ ( ) ( )22

2

0

2222

2

0

0 z2d

z2yxd

−ρφ

=−+φ

=φ

equipotential surfaces: ρ2 – 2z2 = consthyperboloidal shapes⇒

geometry of ring electrode

geometry of endcaps

characteristic trap dimension

minimum radius of ring electrode

minimum distance between endcaps

20

22 z2 ρ=−ρ

20

22 z2z2 −=−ρ

20

20

20 z2d +ρ=

ρ0

2z0

z0

r0

ring electrode

end cap

ρ0

Storage of charged particles in a Penning / Paul trap

BUT: sign of different !

no simultaneous trapping in 3 dimensions possible by purely electrostatic potentials

SOLUTION:

a: superposition of magneticfield in z-direction:

Penning trap

b: time varying voltage (RF) between ring electrode and endcaps:

Paul trap

r

Paul trap geometries

URF

3D confinement

The linear RFQ trap

end cap

ring electrode potential

Equation of motion in a Paul trap

( ) 00 =+∇ rmt,re &&ρφ

( ) 020

000 =+Ω+ ρρ

ρ&&

mtcos VUe

( )02

0

000 =+Ω+

− zz m

tcos VUe&&

ρ

mr = 0··∇

z = 0··

ρ = 0··

equation of motion:

220

00rz mr

Ue8a2aΩ

−=−=t2Ω

=τ ∼ U0substitution:

220

0042

Ω=−=

mrVe

qq rzu = x, y, z ∼ V0

( ) 0u 2cos q2ad

uduu2

2=τ−+

τMathieu differential equation

Ion motion in a Paul trap

Solution for small amplitudes:

( )ρω −

Ω−∝ ttqtu u

u cos cos 2

1)(

macro motion (slow)micro motion (fast, RF)

Ion trajectory

Stable motion only for special combinations of U0 and V0

STABILITY DIAGRAM

Stability diagram of a Paul trap

Principle of Penning traps

Cyclotron frequency: Bmqfc ⋅⋅=

π21

B

q/m

PENNING trapStrong homogeneous magnetic fieldWeak electric 3Dquadrupole field

z0

r0

ring electrode

end cap

Frans Michel Penning(Penning discharge 1936)

Hans G. Dehmelt(Nobel prize in physics 1989)

Confinement in a Penning trap

axial harmonicpotential

radial confinement with magnetic field

Penning trap configurations

mm

Uz (V)

0

50

100

-50

-100

0 40 80

Cylindrical Penning trap

Potentialdistribution

main electrodescorrection electrodes

0

50

100mm

0

5

10

Hyperbolical Penning trap

main electrodescorrection electrodes

Equation of motion in a Penning trap

F = −e0∇φ(r)+v×Bplus Lorentz force:

F = −e0(∇φ(r)+v×B) + mr = 0··equation of motion:

axial oscillation

02

20

00 =+⋅ zmzmd

Ue&&m z = 0··

20

002md

Uez =ω z or axial

frequency

radial oscillation

242

22zcc ωωω

ω −+=+

242

22zcc ωωωω −−=−

modified cyclotronfrequency

magnetronfrequency

iyxu +=

Bme

c0=ω

( ) tieutu ω−= 0

0uu2

ui2z

c =+ω

−ω &&&

substitution:

·u - ·u=

Ion motion in a Penning trap

Motion of an ion is the superposition of three characteristic harmonic motions:– axial motion (frequency fz)– magnetron motion (frequency f–)– modified cyclotron motion (frequency f+)

The frequencies of the radial motions obey the relation

c-+ fff =+

magnetron motion (f-)

modified cyclotronmotion (f+)

axial motion (fz)

zr

r-

r+

Typical frequenciesq = e, m = 100 u,B = 6 T⇒ f- ≈ 1 kHz

f+ ≈ 1 MHz

L.S. Brown, G. Gabrielse,Rev. Mod. Phys. 58, 233 (1986).

3

2

1

0n +

n+

0 1 2

0

n z

n_

Landau levels of an ion in a Penning trap

modifiedcyclotron frequency

axial frequency

magnetron frequency

Energy of harmonic oscillators:

E = ηω+(n++1/2) + ηωz(nz+1/2) - ηω-(n-+1/2)

amplitudes:

<ρ> ∼ n +12

⇒ magnetron motion is unstable !

cooling: quantum number n → 0

Excitation of radial ion motions

Dipolar azimuthal excitationEither of the ion's radial motions can be excited

by use of an electric dipole field in resonancewith the motion (RF excitation)⇒ amplitude of motion increases

without bounds

Quadrupolar azimuthal excitationIf the two radial motions are excited at their

sum frequency, they are coupled⇒ they are continuously converted

into each other

+Ud -Ud

r

r0

Ud

-Uq

-Uq

r0

r

+Uq+Uq

Uq

Magnetron excitation: ρ− Cyclotron excitation: ρ+

Conversion of radial motions

Penning and Paul traps at accelerators

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