Low energy beamline on the new
Storage Ring at MAX-lab
Sverker Werin
MAX-lab
2011-11-09
The aim has been to optimise the radiation from an insertion device in the
wavelength region 5-40 eV and to see how the new 600-700 MeV storage ring
performs relative to MAX II.
A number of type set ups have been analysed at 4, 25 and 40 eV giving the result
that:
The new ring is superior at 4 eV, slightly better at 25, while MAX II is better at
40 eV (and most likely beyond).
At 40 eV the radiation from MAX II has a higher peak flux, while there is no
difference at lower energies.
MAX II gives a significantly higher total power within the acceptance. At 5 eV
up to 200 W.
Table 1. A set of different devices at MAX-lab
Period N Kmax Bmax Gap
MAX II 1.5 GeV 0.1 m 25 10.76 1.15 T 22 mm
MAX B 600 MeV 0.066 m 30 4.40 0.713 T 22 mm
MAX B 700 MeV 0.07 m 28 5.04 0.771 T 22 mm
Model
The radiation of interest here is the radiation that comes to the monochromator
within the physical aperture (entrance slit, acceptance...) and within the energy
resolution (energy window) of the monochromator.
The energy resolution is 1/10.000 which means an energy window with E =
E/10.000. For all practical purposes this window is much smaller than all effects
present in the undulator radiation. We can thus assume that all broadening effects
comes from the undulator and that the radiation across the energy window is
constant.
The radiation coming to a point, p, on the entrance aperture (Figure 1) of the
monochromator has a certain centre energy, EU., different from the energy at the
very centre of the radiation cone: EU .
EU U .
The linewidth at this point, p, is given by contributions from energy spread, the
natural linewidth, beam divergence (and possibly the beamsize), errors in the
undulator.
Let us here neglect the contributions from the beamsize and errors in the
undulator.
The linewidth from the undulator is more or less constant over the emission angles,
and we assume that the same linewidth is present at all points on the aperture.
Both the energy of the
centre point and the
intensity varies with the p
distance to the cone
centre.
The intensity at point p at
the energy of the energy
window in the
monochromator, Em, can
be extracted from the
linewidth and the distance E E EU
m U 0
from the centre energy at
point p.
E U m
Figure 1. Layout
The energy varies like :
1,24 106 1,24 106
EeV 6,24 1018
hc
.
w K 2 2 2
w 2
1
2i 2
2
2i
As EU moves with we can translate the energy intensity distribution to an angular
intensity distribution.
Example:
Lets choose an "ideal case" when Em = EU0 (The monochromator tuned to
the peak of the undulator spectrum), and an optimum opening angle when
the intensity has dropped to 50 % value at EU0. This occurs at the HWHM
point of the linewidth.
The natural linewidth of a 25 pieces of 0.1 m period undulator at first
harmonic is 1/25 = 0.04 (FWHM), and thus the HWHM is at 0.02.
2 2
K2
1
2
which for:K= 5; = 3000 translates into: =0.17 mRad.
In reality the linewidth is larger due
to additional broadening effects. 10 mm MPW on MAX II at 40 eV
4,5E-2
4,0E-2 Natural
When do other broadening 3,5E-2 Divergence
effects come into play? Energy
Relative linewidth
3,0E-2
Total
2,5E-2
Braodening effects that come inte play are
2,0E-2
due to: undulator periods (natural energy
spread), e-beam divergence, energy 1,5E-2
spread and magnetic imperfections in the 1,0E-2
undulator. The last effect is normally
50,0E-4
neglectable. These effects add up to a
total linewidth. 00,0E+0
0 2 4 6 8
Harmonic (i)
In figure 2 there are the linewidths for a 10
mm period undulator on MAX II. We can Figure 2. Linwidths of a 10 mm undulator on MAX II.
2
see that operation at a low harmonic (here at fixed energy) gives a linewidth
dominated by the natural linewidth. While moving up in harmonics the linewidth
changes to be energy spread dominated.
At the first harmonic it is perfectly enough to
New ring, 66 mm Undulator at 25 eV only include the natural energy spread.
3,5E-2
Natural The other example is the 66 mm period
3,0E-2
Divergence undulator on the new ring (figure 3), where
2,5E-2 the situation is very similar to the 10 mm
Realtive linewidth
Energy
Total case on MAX II.
2,0E-2
1,5E-2 One point here is that to do simulations
1,0E-2
including energy spread is difficult as the
standard codes to not include this effect.
50,0E-4
00,0E+0 By only regarding cases using harmonic 3 or
0 1 2 3 4 5 6 lower it is not too bad to neglect the effect of
harmonic (i) energy spread.
Figure 3. Linewidths of an undulator on the new ring.
Results
The results from the simulations are given in the tables on the coming pages. All
important values are within a factor of 3 from each other, except the total power
inside the aperture which is significantly higher for devices utilising MAX II.
The opening angles have been chosen "by eye" to suit the emission cones
resulting from the program. In the same way the "Not On Top" values, which
means that the monochromator has been tuned away from the wavelength of the
undulator peak, to take advantage of a larger integrated flux over the aperture for
these cases, have been chosen "by eye". (figure 4).
Figure 4 a-c. Flux through different opening angles. 30 period, 0.066 m undulator
on the new ring at 25 eV. c) not on top.
20E+14
18E+14
16E+14
14E+14
12E+14
Flux 10E+14
8E+14
6E+14
4E+14
2E+14 0,2
8
00E+0 -0 , mRad
03
5
-0 0
10
5
-0 ,
70
,3
0
35
,2
0
07
-0
,0
21
0
-0
35
0,
0,
0,
mRad
20E+14
18E+14
16E+14
14E+14
12E+14
Flux 10E+14
8E+14
6E+14
4E+14
2E+14 0,1
4
00E+0 -0 ,
01 mRad
75
-0 5
05
7
-0 ,
35
,1
5
17
,1
5
03
-0
,0
5
10
5
-0
17
0,
0,
0,
mRad
16E+14
14E+14
12E+14
10E+14
Flux 8E+14
6E+14
4E+14
2E+14 0,2
8
00E+0 -0 , mRad
03
5
-0 0
10
5
-0 ,
70
,3
0
35
,2
0
07
-0
,0
21
0
-0
35
0,
0,
0,
mRad
4
5 eV
Device Radiation +-0,35 mRad +-0,6 mRad
Booster SR N=30 4,84 eV 5,16e14 5,16e14 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=4,4 On Top 1,71e12 2,08e13 Flux within aperture (100 mA 1/10.000BW)
L=2m 23 23 Total power (W)
=0.066m 1,47 4,32 Power within aperture (W)
Booster SR N=30 4,78 eV 4,76e14 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=4,4 Not On Top 3,15e13 Flux within aperture (100 mA 1/10.000BW)
L=2m 23 Total power (W)
=0.066m 4,32 Power within aperture (W)
Booster SR N=37 4,84 eV 7,75e14 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=4,4 On Top 2,68e13 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 28 Total power (W)
=0.066m 5,32 Power within aperture (W)
MAX II N=25 4,935 eV 6,7e14 6,7e14 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
1500 MeV K=9,2 On Top 1,42e12 1,50e13 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 345 345 Total power (W)
=0.1m 66,2 194 Power within aperture (W)
MAX II N=25 4,80 eV 5,35e14 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
1500 MeV K=9,2 Not On Top 2,81e13 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 345 Total power (W)
=0.1m 194 Power within aperture (W)
5
25 eV
Device Radiation +- 0,175 mR +- 0,35
mRad
Booster SR N=30 24,25 eV 1,80e15 1.8*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=1,5 On Top 1,43e12 1.95*1013 Flux within aperture (100 mA 1/10.000BW)
L=2m 1st harm 2,67 W 2,67 Total power (W)
=0.066m 0,122 W 0,49 Power within aperture (W)
Booster SR N=30 24.0 eV 1.59*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=1,5 Not On Top 2.58*1013 Flux within aperture (100 mA 1/10.000BW)
L=2m 1st harm 2,67 Total power (W)
=0.066m 0,49 Power within aperture (W)
Booster SR N=37 24,25 eV 2.65*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=1,5 On Top 2.55*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 1st harm 2,67 Total power (W)
=0.066m 0,49 Power within aperture (W)
Booster SR N=37 24.00eV 2.22*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=1,5 Not On Top 3.36*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 1st harm 2.67 Total power (W)
=0.066m 0.49 Power within aperture (W)
MAX II N=25 24,8eV 2.79*1015 2.79*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
1500 MeV K=3,9 On Top 1.47*1012 1.63*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 1st harm 62 62 Total power (W)
=0.1m 7.0 27.9 Power within aperture (W)
MAX II N=25 24,4eV 2.45*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
1500 MeV K=3,9 Not On Top 2.62*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 1st harm 62 Total power (W)
=0.1m 27.9 Power within aperture (W)
6
40 eV
Device Radiation +- 0,125 +- 0.25
Booster SR N=30 40,0eV 1,62*1015 1,62*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=2,4 On Top 0,79*1012 1,09*1013 Flux within aperture (100 mA 1/10.000BW)
L=2m 3rd harm 6,8 6,8 Total power (W)
=0.066m 0,1 0,4 Power within aperture (W)
Booster SR N=30 39,7eV 1,23*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=2,4 Not On Top 1,41*1013 Flux within aperture (100 mA 1/10.000BW)
L=2m 3rd harm 6,8 Total power (W)
=0.066m 0,4 Power within aperture (W)
Booster SR N=37 40,0eV 2,36*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
600 MeV K=2,4 On Top 1,43*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 3rd harm 8,4 Total power (W)
=0.066m 0,5 Power within aperture (W)
Booster SR N=37 39,0eV 1,74*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
700 MeV K=2,85 Not On Top 1,82*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 3rd harm 15,3 Total power (W)
=0.07m 1,04 Power within aperture (W)
MAX II N=25 39,9eV 4,3*1015 4,3*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
1500 MeV K=2,95 On Top 1,55*1012 1,56*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 35,5 35,5 Total power (W)
=0.1m 2,7 10,74 Power within aperture (W)
MAX II N=25 39,3eV 3,83*1015 Peak angular flux density (ph/(s mr^2 100mA 0.1%BW)
1500 MeV K=2,95 Not On Top 2,51*1013 Flux within aperture (100 mA 1/10.000BW)
L=2,5m 35,5 Total power (W)
=0.1m 10,74 Power within aperture (W)
7