1. Mike Charlton Physics, Swansea
Antimatter at Low Energies
Mike Charlton Physics, Swansea
Antimatter at Low Energies - Fudan Summer School - July 16

2. Antimatter at Low Energies - Fudan Summer School - July 16
Overview of Lectures
III. Antihydrogen
- Motivation
- Basic formation processes
- Formation and detection of antihydrogen
- Antihydrogen trapping
- Physics with antihydrogen
- Prospects
IV. Applications of Antiparticles
- Use of positrons in condensed matter
- Use of positrons in medicine
- The positron as a sensitive probe in atomic physics
- Positrons in space
- The positive muon
Antimatter at Low Energies - Fudan Summer School - July 16

3. Antimatter at Low Energies - Fudan Summer School - July 16
Overview of Lecture
Antihydrogen
- Motivation
- Basic formation processes
- Formation and detection of antihydrogen
- Antihydrogen trapping
- Physics with antihydrogen
- Prospects
Antimatter at Low Energies - Fudan Summer School - July 16

4. Antimatter at Low Energies - Fudan Summer School - July 16
Motivation
Antimatter at Low Energies - Fudan Summer School - July 16

5. Antihydrogen Formation Mechanisms
Spontaneous Radiative Recombination (SRR)
Stimulated Radiative Recombination
Three-Body Recombination (TBR)
The Positronium Reaction
We will take a brief look at SRR, TBR and the Positronium Reaction
Antimatter at Low Energies - Fudan Summer School - July 16

6. Antihydrogen Formation Mechanisms
Spontaneous Radiative Recombination (SRR) ─
Antimatter at Low Energies - Fudan Summer School - July 16

7. Antihydrogen Formation Mechanisms
The radiative process, cross section quoted by Holzscheiter, Charlton and Nieto, Phys. Rep. 402 (2004) 1
Antihydrogen principal quantum number
nH = 1 binding energy
Kinetic energy of e+ in antiproton rest frame
The formulae apply for Ee << E0 and clearly favour low nH.
Antimatter at Low Energies - Fudan Summer School - July 16

8. Antihydrogen Formation Mechanisms
We can now go on to estimate a “total” radiative cross section and attempt to construct a rate for the reaction.
Positron and antiproton spatial density profiles
This is the phase space overlap of the positron and antiproton clouds
Positron velocity distribution
This is the recombination rate coefficient
Antimatter at Low Energies - Fudan Summer School - July 16

9. Antihydrogen Formation Mechanisms
To proceed we need to make assumptions about the densities, the overlap of the clouds and the velocity distribution …. We usually take the easy route and assume complete and constant overlap with constant density clouds with Maxwellian temperature distributions.
N.B. This isn’t necessarily the situation that pertains to the experiments, but it is a start … here we find,
Antiproton number Positron density Averaged rate coefficient
Under these conditions the rate of events, per antiproton, can be found from (see e.g. Stevefelt et al, Phys Rev A 12 (1975) 1246)
per second with Te in K and ne in cm-3
Antimatter at Low Energies - Fudan Summer School - July 16

10. Antihydrogen Formation Mechanisms
Three-Body Recombination (TBR) + + e
Two unbound positrons with an antiproton. The positrons undergo an elastic collision;
Energy change ΔE ~ E ~ kTe
The length scale for this reaction is governed by the length scale of the interactions. This is the Thomson length, RT, found by equating thermal and Coulomb energies as –
Antimatter at Low Energies - Fudan Summer School - July 16

11. Antihydrogen Formation Mechanisms
This is not the end of the story for the TBR since an extra collisional-radiative term needs to be added to those for SRR and TBR. This is empirically determined and is due to radiative decay of some of the high-lying states formed in TBR. The full rate looks like
This rate is for full overlap, in equilibrium and with no applied fields … so there are many further things to consider … Also the antihydrogen formed by the TBR is weakly bound and can be field ionized in plasma/trap fields, or in collisions. Thus, there may be a reaction cycle of the form
…this can be an important antiproton transport mechanism …
Antimatter at Low Energies - Fudan Summer School - July 16

12. Antihydrogen Formation Mechanisms
Basic comparator of the SRR and TBR
Radiative Three-body
Rate T dependence T T-4.5
Final state n < n >> 10
Stability (re-ionization) high low
Expected rates ~10s Hz fast ???
Lets have a look at an example
Antimatter at Low Energies - Fudan Summer School - July 16

13. Antihydrogen Formation Mechanisms
CAUTION!!
3-body and radiative labels reversed!!
Around 100 K
Thanks to Paul Bowe, Aarhus, for this plot and numerous discussions
Antimatter at Low Energies - Fudan Summer School - July 16

14. Antihydrogen Formation Mechanisms (Simulations)
Binding energies
Antimatter at Low Energies - Fudan Summer School - July 16

15. Antihydrogen Formation Mechanisms (Simulations)
Time evolution of antihydrogen formation positions
1015m-3
5x1013m-3
At the higher ne the repeated formation and destruction of antihydrogen results in radial transport of the antiprotons to the plasma edge
Antimatter at Low Energies - Fudan Summer School - July 16

16. Antihydrogen Formation Mechanisms
First suggested some time ago: Humberston et al, J. Phys. B 20 (1987) L25
Importance of excited states pointed out: Charlton, Phys. Letts A 143 (1990) 143
The scaled (principal quantum number to the 4th power) cross sections for antihydrogen formation and Ps destruction. The velocity scale is in terms of the quasi-classical orbit speed of the positron in the positronium.
Antimatter at Low Energies - Fudan Summer School - July 16

17. Antihydrogen Formation Mechanisms
Antimatter at Low Energies - Fudan Summer School - July 16

18. Antihydrogen Formation Mechanisms
Double Rydberg charge exchange method; Hessels et al, Phys. Rev. A 57 (1998) 1668
Implemented by ATRAP: Storry et al., PRL, 93 (2004)
Antimatter at Low Energies - Fudan Summer School - July 16

19. Antihydrogen Production and Detection
Sympathetic compression of an antiproton cloud by electrons
Typically use a fixed frequency rotating wall technique at 10 MHz
G. Andresen et al., PRL, 101 (2008)
Antimatter at Low Energies - Fudan Summer School - July 16

20. Antihydrogen Production and Detection
Evaporative cooling of antiproton and positrons to lower temperatures prior to mixing
9 K
23 K
19 K
325 K
57 K
1040 K
Typically (9 ± 4) K is lowest achievable at the lowest well available at which (6 ± 1) % of the initial antiprotons remain
Andresen et al., PRL (2010)
Antimatter at Low Energies - Fudan Summer School - July 16

21. Antihydrogen Production and Detection
Nested Penning trap arrangement; Gabrielse et al, Phys. Letts A129 (1988) 38
Antimatter at Low Energies - Fudan Summer School - July 16

22. Antihydrogen Production and Detection
Autoresonant injection of antiprotons in to the positron plasma to achieve robust mixing with minimum added kinetic energy
Chirped driven harmonic oscillator
Andresen et al. PRL (2011)
Antimatter at Low Energies - Fudan Summer School - July 16

23. Antihydrogen Production and Detection
Antimatter at Low Energies - Fudan Summer School - July 16

24. Antihydrogen Production and Detection
Antimatter at Low Energies - Fudan Summer School - July 16

25. Antihydrogen Production and Detection
Antimatter at Low Energies - Fudan Summer School - July 16

26. Antihydrogen Production and Detection
a) Antiproton annihilation
b) Cosmic ray
Antimatter at Low Energies - Fudan Summer School - July 16

27. Antihydrogen Production and Detection
Potential energy surface of an electron/positron in a combined Coulomb and static electric field in the z-direction: from Lankhuijzen and Noordam, Adv. At. Mol. Opt. Phys. 38 (1997) 121
Antimatter at Low Energies - Fudan Summer School - July 16

28. Antihydrogen Production and Detection
ATRAP
Field ionized antiprotons
None present without e+
Gabrielse et al., PRL 89 (2002)
Antimatter at Low Energies - Fudan Summer School - July 16

29. Antihydrogen Trapping
Exploit the magnetic moment of the atom
μ is the Bohr magneton, μB, for the ground state
Breit-Rabi diagram for the ground state of hydrogen
Antimatter at Low Energies - Fudan Summer School - July 16

30. Antihydrogen Trapping
Classic Ioffe-Pritchard Geometry
quadrupole winding
Mirror coils
Based on Berkeley/Swansea results: standard quadrupole arrangement was rejected by ALPHA as the magnetic field gradient across charged plasmas is too great;
see Fajans et al., Phys. Rev. Lett (2005)
Antimatter at Low Energies - Fudan Summer School - July 16

31. Antihydrogen Trapping
In general for a multipole of order m (i.e. a quadrupole has order 2, and octupole order 4)
The radial dependence goes as follows with Bw the field at the Penning trap wall, at a radius, Rw
Quadrupole B
Octupole
Radius in trap
Antimatter at Low Energies - Fudan Summer School - July 16

32. Antihydrogen Trapping
N.B.
Well depth ~ 0.7 K/T
Technical details of the trap in Bertsche et al, NIM A 566 (2006) 746
Antimatter at Low Energies - Fudan Summer School - July 16

33. Antihydrogen Trapping
30,000 pbars at 200K
2M positrons at 40 K (evaporatively cooled)
Auto-resonant injection and mix for 1 sec.
Clear the charge particles
Turn off the neutral trap (1/e time ~ 9 ms)
Search for pbar annihilations from Hbar (bias fields to eject any charged particles still trapped)
Antimatter at Low Energies - Fudan Summer School - July 16

34. Antihydrogen Trapping
Published in Nature 468 (2010) 673
Initial publication – 38 events
Antimatter at Low Energies - Fudan Summer School - July 16

35. Antihydrogen Trapping
309 events – Nature Physics 7 (2011) 558
Antimatter at Low Energies - Fudan Summer School - July 16

36. Antihydrogen Trapping
309 events – Nature Physics 7 (2011) 558
Antimatter at Low Energies - Fudan Summer School - July 16

37. Physics with Antihydrogen
Antimatter at Low Energies - Fudan Summer School - July 16

38. Physics with Antihydrogen
On resonance – 15 MHz scan width for 15 s each – 6 repeats
Antimatter at Low Energies - Fudan Summer School - July 16

39. Physics with Antihydrogen
On resonance – 15 MHz scan width for 15 s each – 6 repeats
Off resonance – B shift
Antimatter at Low Energies - Fudan Summer School - July 16

40. Physics with Antihydrogen
On resonance – 15 MHz scan width for 15 s each – 6 repeats
Off resonance – B shift
On resonance – frequency shift
Antimatter at Low Energies - Fudan Summer School - July 16

41. Physics with Antihydrogen
Extra annihilations on resonance – the microwaves force the antihydrogen into the untrapped states
First observation of a resonant quantum transitions in an anti-atom: Nature 483 (2012) 439
Antimatter at Low Energies - Fudan Summer School - July 16

42. Physics with Antihydrogen
Analysis of the up/down annihilation positions versus time (red dots, data: green dots, simulations) during the magnet shutdown
F = Mg/M, ratio of grav. to inertial mass
C. Amole et al., Nature Comm. 4 (2013) 1785
Antimatter at Low Energies - Fudan Summer School - July 16

43. Physics with Antihydrogen
ALPHA’s reverse cumulative average analysis
Data
Red: y-direction
Green: x-direction
Simulations
Dash: “antigravity” at given |F|
Line: gravity at given |F|
Grey bands: 90% confidence limits on simulations
C. Amole et al., Nature Comm. 4 (2013) 1785
Antimatter at Low Energies - Fudan Summer School - July 16

44. Physics with Antihydrogen
Antimatter at Low Energies - Fudan Summer School - July 16

45. Antimatter at Low Energies - Fudan Summer School - July 16
Prospects
Antimatter at Low Energies - Fudan Summer School - July 16

46. Antimatter at Low Energies - Fudan Summer School - July 16
Prospects
System for 1S-2S laser spectroscopy
Antimatter at Low Energies - Fudan Summer School - July 16

47. Antimatter at Low Energies - Fudan Summer School - July 16
Prospects
A very bright and busy future awaits …
CERN has started work on ELENA an extra ring to decelerate antiprotons to about 100 keV – this will increase our capture efficiency for low energy antiprotons by a factor of around 100.
Antimatter at Low Energies - Fudan Summer School - July 16