Experimental investigations of synchrotron radiation at the onset of the quantum regime

The classical description of synchrotron radiation fails at large Lorentz factors, $\gamma$, for relativistic electrons crossing strong transverse magnetic fields $B$. In the rest frame of the electron this field is comparable to the so-called critical field $B_0=4.414\times {10}^9\mathrm{T}$. For $\chi =\gamma B/B_0\simeq 1$ quantum corrections are essential for the description of synchrotron radiation to conserve energy. With electrons of energies 10–150 GeV penetrating a germanium single crystal along the $⟨110⟩$ axis, we have experimentally investigated the transition from the regime where classical synchrotron radiation is an adequate description, to the regime where the emission drastically changes character; not only in magnitude, but also in spectral shape. The spectrum can only be described by quantum synchrotron radiation formulas. Apart from being a test of strong-field quantum electrodynamics, the experimental results are also relevant for the design of future linear colliders where beamstrahlung—a closely related process—may limit the achievable luminosity.

Figure 1

The differential radiation spectrum from an electron traversing a Ge $⟨110⟩$ crystal at 280 K entering the crystal along the axis for different electron energies. The curves have been calculated with Eq. (17.7) in Ref. [9]. $\Delta t=\Delta l/c$ is the time it takes to traverse the $200\mu \mathrm{m}$ crystal used in the experiment.

Figure 2

The integral radiation intensity in axial alignment [calculated with Eq. (17.15) 9] divided by the Bethe-Heitler radiation for different electron entrance angles and as a function of the energy $E$ of the impinging electron.

Figure 3

For a uniform particle distribution traversing a Ge crystal along the $⟨110⟩$ axis is shown the fraction of particles that experience a field $\chi /{\chi }_s$ or above.

Figure 4

Experimental setup (not to scale). An electron beam enters from the left. DC refers to drift chambers and Sc to scintillators. Xtal is the Ge crystal ($0.87\%X_0$), ScH a hole scintillator ($ø12\mathrm{mm}$), MBPL the deflection magnet, Cu a copper converter, SSD a solid-state detector, MDX the second deflection magnet and Lg refers to lead glass calorimeters (J for Jura and S for Salève—landmarks near Geneva—and C for center). Dashed boxes indicate vacuum pipes. The overall length is around 60 meters from the first scintillator to the lead glass detectors. All distances on the figure are between adjacent DCs.

Figure 5

Left: Lead glass measurements for 120 GeV electrons at level 1 and 2 for no target and random position with Bethe-Heitler fits. The fits include a pile-up correction [14]. Right: No target subtracted from random at level 1 and 2 to see the radiation from the nonaligned crystal.

Figure 6

Monte Carlo simulations (red crosses) and random data (blue dots) for 120 GeV electrons at level 2 (left) and level 3 (right). At level 2 the simulation has been scaled with 0.11 and at level 3 with 0.045.

Figure 7

Pair spectrometer efficiency at levels 2 and 3 for 120 GeV data. The efficiency includes the conversion probability from the Cu converter.

Figure 8

Differential radiation spectra for 10, 20, 50, 100, 120, and 150 GeV electrons along the Ge $⟨110⟩$ axis for LG and PS measurements. Theoretical calculations based on formulas by Baier et al. [9] are also plotted. The error bars only represent statistical uncertainties.

Figure 9

Radiation enhancement as a function of photon energy for PS L3 (black solid) and LG data (black dashed). The theoretical enhancement (red thick line) calculated with Baier’s formulas agrees well with the PS data.

Figure 10

The integral radiation enhancement as a function of electron energy for PS L3 (black thick solid) and LG data (black thick dashed). The theoretical integral enhancement calculated with Baier’s formulas and including detection energy thresholds for PS L3 (red thin solid) and LG (red thin dashed) is also shown.

Figure 11

The radiation enhancement as a function of the associated strong-field parameter ${\chi }_s$ for a Ge $⟨110⟩$ crystal detected by a lead glass calorimeter and W $⟨111⟩$ lead glass measurements [4]. The data have been fitted by the approximate quantum suppression formula, Eq. (7), as described in the text. A theoretical calculation including energy loss for the W data is also plotted.

Figure 12

100 GeV PS data with theoretical calculations. The CFA has been fitted to the data (black solid line) and we find $\chi =0.68\pm 0.16$. The CFA without the spin contribution has been plotted with the parameters found from the CFA fit (black dotted) and the classical synchroton radiation spectrum has been plotted for the same field (blue dash-dotted).