Crystal Undulators as a New Type of Gamma-Ray Source

Ulrik I. Uggerhøj Department of Physics and Astronomy

Aarhus University, Denmark

On behalf of the collaborations CERN NA63 and SLAC E-212

Strong field effects - crystalline targets

Strong fields

• The critical field:

•Strong – compared to what?

Relativistic invariant:

‘Schwinger-field’ (Sauter’s field)

Radiation emission

Crystalline fields: 1010-11 V/cm

Rev. Mod. Phys. 77, 1131 (2005)

Radiation emission

Classical -> Quantum

synchrotron

Other examples: Pair production Polarization Spin-flip Trident production Birefringence

Beamstrahlung – synchr.rad.

-4 -2 0 2 4

0.0

0.2

0.4

0.6

0.8

1.0

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log10

(1/), log10

(C)

Synchrotron radiation

Blankenbecler & Drell, eq. (7.5)

From their paper

Our curves, supported by meas. in crystals

Formation length effects - amorphous targets

Bethe-Heitler

LPM

What is the bremsstrahlung transition from single-scattering (BH) to multiple-scattering (LPM)?

Logarithmic t dependence

’Radiation per interaction as a function of number of scatterings’

Transition between Bethe-Heitler and LPM regimes:

PRD 81, 052003 (2010)

Structured targets

Measuring the formation length with a micrometer screw....

Crystalline undulators

Transverse energy states Harmonic potential for positrons equidistant transverse energy states ‘Population inversion’ from high-lying transverse energy states

Doppler-shift back to the lab => another factor 2

Lorentz boost => a factor

(110) (110)

Enhancements of 80-100...

Measurements in Si (1980’s), event-based

Radiation cooling

Qualitative agreement with measurements

Radiation cooling for diamonds of >1 cm (?)

Based on ideas from: Z. Huang, P. Chen and R.D. Ruth, Nucl. Instr. Meth. B 119 (1996), 192

Undulator Radiation from Positron Channeling in a Single Crystal

A. Solov’yov, A. Korol, W. Greiner et al.

Crystalline undulator radiation (?)

C 34, 175 (2011)

Electrons

Large amplitude, long period (LALP): Small amplitude, short period (SASP):

‘Violet laser’

Calculations for other amplitudes

Narrowing ChR, increasing undulator radiation:

Positrons Electrons 10 GeV, 12 μm Si, a=0.4 Å

_____ incl. Quantum corr. -------- excl. Quantum corr.

Gamma-ray ‘klystron’

Other possible routes to a gamma-ray laser: Bose-Einstein condensation of Positronium atoms (lead proponent A.P. Mills, UC Riverside). Main challenge is short lifetime (142 ns)

Calculations by T. Wistisen Next step is to include radiation cooling (likely to increase expected gain further)

Gamma-ray laser?

GDR energies

Calculated peak brilliance of a LALP crystalline undulator

First harmonic

Complementary to other radiation sources

GDR energies Assumes lasing

Undulator Radiation from Channeling in a Single Crystal

A possible route to a gamma-ray laser?

LALP

SASP

SLAC E-212

‘Violet laser’