Short period, high field cryogenic undulator for extreme performance x-ray free electron lasers

Short period, high field undulators can enable short wavelength free electron lasers (FELs) at low beam energy, with decreased gain length, thus allowing much more compact and less costly FEL systems. We describe an ongoing initiative to develop such an undulator based on an approach that utilizes novel cryogenic materials. While this effort was begun in the context of extending the photon energy regime of a laser-plasma accelerator based electron source, we consider here implications of its application to sub-fs scenarios in which more conventional injectors are employed. The use of such low-charge, ultrashort beams, which has recently been proposed as a method of obtaining single-spike performance in x-ray FELs, is seen in simulation to give unprecedented beam brightness. This brightness, when considered in tandem with short wavelength, high field undulators, enables extremely high performance FELs. Two examples discussed in this paper illustrate this point well. The first is the use of the SPARX injector at 2.1 GeV with 1 pC of charge to give 8 GW peak power in a single spike at 6.5 Å with a photon beam peak brightness greater than ${10}^{35}\mathrm{photons}/(\mathrm{s}{\mathrm{mm}}^2{\mathrm{mrad}}^{2}0.1\%\mathrm{BW})$, which will also reach LCLS wavelengths on the 5th harmonic. The second is the exploitation of the LCLS injector with 0.25 pC, 150 as pulses to lase at 1.5 Å using only 4.5 GeV energy; beyond this possibility, we present start-to-end simulations of lasing at unprecedented short wavelength, 0.15 Å, using 13.65 GeV LCLS design energy.

Figure 1

Magnetization curves for the $({\mathrm{Nd}}_{0.2},{\mathrm{Pr}}_{0.8}{)}_2{\mathrm{Fe}}_{14}\mathrm{B}$ magnets at 30 K (dashed line) and 300 K (solid line). The large increase in coercivity and energy product when the magnet is cooled can be seen.

Figure 2

Simulation results for the 9 mm period undulator when cooled to 30 K, showing the effective magnetic field, given by $B_{\mathrm{eff}}=\sqrt{\sum _{}^{}(B_n^2/n^2)}$. The difference between the two curves at large gap can be nearly entirely accounted for by the difference in simulated undulator length while segmentation limits in Radia prevent more accurate comparison at the small gap ($<2\mathrm{mm}$). The black diamond shows the assumed working point. $K_{\mathrm{eff}}=0.84B_{\mathrm{eff}}$.

Figure 3

Praseodymium magnet design with samarium-cobalt sheath. Part (a) shows one quarter of an undulator period. The red samarium-cobalt sheath surrounds the more easily demagnetized, at room temperature, orange praseodymium magnet. Half of the blue steel pole has been cut away to reveal the structure of the assembly. Part (b) is an exploded view of (a) which shows that the bottom pieces of samarium-cobalt are used to fill in the chamfers of the praseodymium magnet. This is useful because having more strong magnet material near the beam axis promotes field quality. Although the chamfer samarium-cobalt fill-ins are naturally attracted to the praseodymium magnets, some form of adhesive or mechanical restraint will be required. From an engineering standpoint it is easier to replace the fill-ins with a full strip of samarium-cobalt and make the praseodymium magnet a simple block.

Figure 4

Beam profile of the SPARX ultrashort beam as generated with start-to-end simulations.

Figure 5

GENESIS simulation results for the SPARX ultrashort low-charge case. Part (a) shows the exponential high gain regime saturating at 10 m of undulator, the regions of zero gain are due to the significant gaps between undulators reserved for the strong focusing quadrupoles and diagnostics. Part (b) shows the gain as a function of distance along the beam, the knee in the charge profile (Fig. 4) creates a similar knee in the radiation longitudinal profile. Part (c) shows the spectrum of the output radiation. The radiation has extremely narrow bandwidth.

Figure 6

Harmonic gain of the SPARX ultrashort low-charge beam lasing in the cryogenic hybrid praseodymium undulator.

Figure 7

(a) GENESIS simulation results for the 4.5 GeV LCLS beam. The saturation length of the fundamental mode is 15 m with a gain length of 70 cm. (b) At saturation the beam shows three spikes in the longitudinal profile, consistent with a 11 nm cooperation length [45]. (c)  The fundamental interaction wavelength is just over 1.42 Å.

Figure 8

(a) GENESIS simulation of a 13.65 GeV LCLS beam traveling through the cryogenic high field undulator. Saturation occurs in 40 m. The incredibly short fundamental wavelength, 0.15 Å (c), does not allow single-spike operation (b).

Figure 9

GENESIS simulation of the 20 pC, 2 fs rms pulse length beam at LCLS, full LCLS energy (14.3 GeV). Violation of the Pellegrini criterion causes dramatic growth in the gain length.

Figure 10

GENESIS simulation of the LCLS 20 pC beam at derated energy of 4.5 GeV, compliance with Pellegrini criterion reestablished.

Figure 11

GENESIS results for the ($T^3$) SASE FEL. (a) Saturation occurs in 3 m. (b) The soft x-ray energy is distributed fairly uniformly over the entire length of the pulse. (c) The spectral makeup if the beam is noisy, expected from such a large emittance beam.