Electron Beam Dynamics

Results of PARMELA electron beam simulations showing beam phase space properties at exit of photoinjector.


Electron beam production, acceleration, and transport contains a number of challenges in order to meet our goals of producing the brightest possible x-ray beam.  The electron bunch charge should be as large as possible of course to maximize x-ray flux but is constrained by the needs for small emittance and short bunch length in order to produce bright x-rays, as well as charge-dependent effects of beam loading and wakefields in the RF structures. The maximum bunch charge is also limited by the available cathode-laser power and the cathode quantum efficiency.  The emittance requirement is set so that the electron divergence at the micron sized focus at the laser interaction point has minimal impact on the x-ray bandwidth.  The bunch length during acceleration should be limited to a few RF degrees (less than 1 picosecond at 9.3 GHz RF frequency) so that the energy spread remains small.

The blowout mode of generating an ellipsoidal bunch distribution from the cathode is used for its ability to generate short bunches with a uniform charge distribution that exhibits linear space charge forces thus avoiding emittance growth.  These bunches are well suited for temporal compression and show excellent focusing characteristics for producing micron-sized spots at the interaction point.  The blowout method reduces sensitivity to laser temporal pulse shaping and inhomogeneities in the cathode emission.  Furthermore, because the transverse space charge forces are not only linear, but also identical in each time slice, there is little relative rotation of the timeslices in phase space so that emittance compensation schemes are less critical.

To properly set up the dynamics of the blowout mode the space charge field near the cathode must be much smaller than the applied RF field, but large enough that the bunch length at the gun exit is significantly longer than its initial value. In the thin disk approximation the peak space charge field is  where Q is the bunch charge, r is the bunch edge radius, andis the free-space permittivity.  The RF field at the time of emission is 140 MV/m X sin(50) = 108 MV/m satisfying the first condition.  Numerical simulations indicate that the second condition is satisfied as the RMS bunch length increases from 65 fs to 260 fs at the gun exit, resulting in a peak current of 120 A for a bunch charge of 100 pC.  The simulations also show that the bunch has expanded into the desired ellipsoidal distribution at an energy of 3 MeV. 

Results of PARMELA electron beam simulations showing beam phase space properties at laser interaction point.  Beam is focused to a spot a few microns in diameter for efficient, bright x-ray production.

The electron beam exiting the gun is focused by a solenoid magnet to a soft waist at the linac entrance to match the Ferrario criterion for emittance correction, i.e. generating a bunch with time slices that are well-aligned in phase space, resulting in a low overall projected emittance at the linac exit.  The short standing-wave linac then accelerates the bunch to the energy required for x-ray production, 17.8 MeV in the case of 12.4 keV x-rays. Downstream of the linac are a quadrupole pair to match into a 4-magnet chicane that is used primarily to block unwanted stray electrons from entering the laser interaction area using energy and spatial filtering.  The chicane can also be used for bunch compression to produce electron bunches less than 100 fs in duration.  Following the chicane, a short focal length quadrupole triplet focuses the electrons to a small spot at the laser interaction point. The electron beta function is 1.5 mm at the interaction point in both transverse dimensions compared with maximum beta functions at the triplet of about 100 m for a beam size demagnification of a few hundred.