STI Memorandum

 

TO:                        Wayne Kimura

COPIES TO:         Distribution

FROM:                  Dave Quimby

SUBJECT:             Configuration of Second-Stage IFEL Wiggler

DATE:                   5 April 2000



As Wayne forecast in his email of 3 April 2000 [1], the IFEL simulation model has been modified to simulate a second permanent-magnet wiggler IFEL stage. The objectives are to determine the expected second-stage performance and to examine whether tapering the wiggler would be useful. The nominal parameters assumed for simulating this second wiggler are listed in Table 1.

 

Table 1. Nominal simulation parameters for Second Stage IFEL

 

Laser Power                                         400 MW

Laser Beam Radius (w)                        1 mm

Laser Wavelength                                 10.6 mm

Wiggler Length (effective)                     26.4 cm

Wiggler Period                         33 mm

Wiggler B-Field                                    configure as needed

E-Beam Energy                                    45.6 MeV (g = 90.3)

 

The assumed e-beam phase space distribution at the entrance to the second wiggler is based on an earlier simulation completed by Wayne for the current nominal conditions of the STELLA experiment. The beam is assumed to have an energy modulation of ±0.5% and to be optimally pre-bunched, neglecting space charge.

 

Various possibilities for linear tapering the wiggler were examined. As discussed by Wayne [1], up to 2% energy taper could be used. The best settings for adjusting the relative phase and energy of the electron micro-bunches were determined. Approximately optimal settings are listed in Table 2.


 

Table 2. Near-Optimum Beam Injection Parameters for Second Stage IFEL.
(Taper values are % resonant energy change, Dgr/gr.)

 

Parameter                                           0% Taper       2% Taper

Bunch Phase                                         -45°                 -40°

Relative Bunch Energy (Dg/gr)   -1.5%              0.0%

 

Figure 1 shows the calculated energy gain of the micro-bunches as a function of laser power. It is found that the untapered wiggler can actually produce larger acceleration than the tapered wiggler. Evidently this is because the wiggler is so short and the available laser power is sufficiently limited that tapering is not particularly useful.

 

Figure 1.

 

Figure 2 shows the calculated phase space distributions for the untapered case. Note that the second wiggler is to be configured such that the electron micro-bunch enters below resonance and is swept upward in phase space. In the electron energy spectrum the accelerated micro-bunch is superposed upon a very broad background, but should be readily detectable above the background provided that the pre-bunching is reasonably efficient.

 

At the nominal laser power of 400 MW the bucket full-height for the untapered wiggler is about 7%. However, the wiggler is so short that there is less than 1/3 of a synchrotron period within the wiggler length. Thus it is not possible to accelerate the electrons by the full bucket height. Furthermore, since the untapered wiggler is not saturated (there is <½ synchrotron period), there is no real benefit to be obtained by tapering.


Figure 2. Calculated phase space distributions at wiggler entrance and exit for nominal simulation parameters and untapered wiggler.

 

 

 

 

Thus we recommend using a uniform, untapered wiggler for the second stage. Recommended parameters are listed in Table 3.

 

Table 3. Target Parameters for Second Stage IFEL Wiggler.

Parameter                                           1st Stage          2nd Stage

Period                                                  33 mm              33 mm

Number of poles                                   20                    20

Resonant gamma                                  90.3                 91.7 (1.5% larger)

Resonant energy                                   45.6 MeV        46.3 MeV

Wiggler parameter, K                           2.91                 2.97

Effective field                                        0.945T             0.964T

Peak field                                             0.986T             1.006T (est.)

Magnetic gap                                        8.14 mm           7.93 mm (est.)

 

We have also examined the sensitivity to the values used to setting the relative phase and energy of the electron micro-bunches at the entrance to the second-stage wiggler. Results are shown in Figure 3. The nominal recommended operating point is not near any “cliffs.” The proper relative energy should be set by offsetting the resonant energy of the second wiggler from that of the first as indicated in Table 3 and by matching the e-beam energy to resonate with the first wiggler. The proper phasing in the second stage should be obtainable simply by optimizing the observed acceleration of the micro-bunches.

 


Figure 3. Calculated sensitivity to phase and energy of injecting micro-bunches
into second stage IFEL.

 

 

 

 

Reference

 

[1] W. Kimura, “Second Permanent-Magnet IFEL,” email dated 4/3/00.