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Define Field Errors

Field errors can be entered as relative or absolute errors. Different multipole components can be specified with different kinds of errors (relative or absolute). If an attempt is made to assign both a relative and an absolute error to the same multipole component, the absolute error is used and a warning is given. Relations between absolute and relative field errors are listed below.

All field errors are specified as the integrated value $\int K_k ds$ of the field components along the magnet axis in $\mathrm{m}^{-k}$ . At present field errors may only affect field components allowed as normal components in a magnet. This means for example that a dipole may have errors of the type dipole, quadrupole, sextupole, and octupole; but not of the type decapole. There is no provision to specify a global relative excitation error affecting all field components in a combined function magnet. Such an error may only be entered by defining the same relative error for all field components.

First the elements to be affected must be selected by the SELECT command. Field errors can then be specified for magnetic elements by one of the statements


EFIELD,ORDER=integer,RADIUS=real,ROT=deferred-vector,
       DKR=deferred-vector,DK=deferred-vector;
EFCOMP,ORDER=integer,RADIUS=real,
       DKN=deferred-vector,DKS=deferred-vector,
       DKNR=deferred-vector,DKSR=deferred-vector;

Each new EFIELD or EFCOMP statement replaces the field errors for all selected elements. Any old field errors present in the range are discarded or incremented depending on the setting of ERROR,ADD. EFIELD defines the error in terms of relative or absolute amplitude and rotation; while EFCOMP defines them in terms of relative or absolute components.

Both commands have the attributes:

ORDER: If relative errors are entered for multipoles, this defines the order of the base component to which the relative errors refer. The default is zero.
RADIUS: Radius were the relative components are specified (default 1 m). This attribute is required if any relative component is used.

The command EFIELD has the following additional attributes:

DK: A vector of deferred expressions. Its component is the absolute error amplitude for the multipole strength with -poles (default: $0 \mathrm{m}^k$ ).
DKR: A vector of deferred expressions. Its component is the relative error amplitude for the multipole strength with -poles (default: $0 \mathrm{m}^k$ ).
ROT: A vector of deferred expressions. Its component is the rotation angle for the multipole strength with -poles (default: 0 rad).

The command EFCOMP has the following additional attributes:

DKN: A vector of deferred expressions. Its component is the absolute error for the normal multipole strength with -poles (default: $0 \mathrm{m}^k$ ).
DKS: A vector of deferred expressions. Its component is the absolute error for the skew multipole strength with -poles (default: $0 \mathrm{m}^k$ ).
DKNR: A vector of deferred expressions. Its component is the relative error for the normal multipole strength with -poles (default: $0 \mathrm{m}^k$ ).
DKSR: A vector of deferred expressions. Its component is the relative error for the skew multipole strength with -poles (default: $0 \mathrm{m}^k$ ).

All random vectors have an unlimited length.

Examples:


EFIELD,DK={0,0.0025*RANF(),0,0,0,DK(5)=0.0092*GAUSS()};
EFIELD,DKR={0,0,0,0.0025*RANF(),0,DKR(5)=0.0092*GAUSS()};