LCLS Conceptual Design Report - Stanford Synchrotron Radiation ...

8.5.2.1 Two-Dimensional Model
L C L S C O N C E P T U A L D E S I G N R E P O R T
In the magnetic design process, two-dimensional modeling is used for the initial scoping of
the problem. The relative thicknesses (parallel to the beam direction) of the magnet and pole are
determined, along with the heights of the magnet and pole. The details of the chamfering at the
tips of the magnet and pole are also determined. These parameters are set so that the effective
magnetic field on axis is a maximum, while ensuring that the demagnetizing field on the magnet
does not become excessive. In the 2D model, the demagnetizing field is worst at open gap.
Figure 8.8 shows the demagnetizing field throughout the magnet. The worst is predicted to be
12.713 kOe, in the region of the magnet chamfer. This is about 1.11 times the magnet coercivity
bHc of 11.4 kOe. The typical magnet specification that has been used in the past required that the
magnet not demagnetize below 1.2 × Hc, so this allows ample margin. The margin is even greater
for the high-coercivity magnet grade that will be used.
The other feature of the magnetic model that is checked in the 2D calculations is the value of
µ in the magnet at closed gap. Figure 8.9 shows the calculated value of the permeability µ in the
pole where it is 90 or below, i.e., where the pole is nearing saturation, for a gap of 6 mm. The µ in
the pole is shown to be 90 or higher everywhere except in the chamfered corner, and the
minimum µ that extends across the pole is 90. Although there may be some small redistribution
of the flux due to the saturation near the pole chamfer, the central region of the pole still serves
well as a flux conduit.
Demagnetizing field in magnet at open gap. 2D model.
Y [mm]
35.0
30.0
25.0
20.0
15.0
10.0
5.0
2
0.0
0.0 5.0 10.0 15.0 20.0
1
25.0 30.0 35.0 40.0 45.0 50.0 55.0
X [mm]
Component: HY
6325.56 9519.17 12712.8
UNITS
Length : mm
Flux density : gauss
Field strength : oersted
Potential : gauss-cm
Conductivity : S cm -1
Source density : A cm -2
Power : erg s -1
Force : dyne
Energy : erg
Mass : g
PROBLEM DATA
f3026o.st
Linear elements
XY symmetry
Vector potential
Magnetic fields
Static solution
Scale factor = 1.0
3462 elements
1849 nodes
4 regions
9/May/2000 17:35:15 Page 10
OPERA-2d
Pre and Post-Processor 7.1
Figure 8.8 A quarter-period model of the magnet structure showing the demagnetizing field in the
magnet, in the 2-D model, at open gap. The particle beam would travel up the page on
the left, in what is labeled here as the ‘y’ direction. The half-pole is on the bottom
here, and the half-magnet on top.
U N D U L A T O R ♦ 8-23