FFAG¶
-
class
zgoubidoo.commands.magnetique.FFAG(label1: str = '', label2: str = '', *params, **kwargs)[source]¶ Bases:
zgoubidoo.commands.magnetique.PolarMultiMagnetFFAG magnet, N-tuple.
Zgoubi manual description
FFAGworks much likeDIPOLESas to the field modelling, apart from the radial dependence of the field, \(B = B_0 (\frac{r}{r_0})^k\), so-called “scaling”. Note thatDIPOLESdoes similar job by using a Taylor r-expansion of \(B_0(\frac{r}{r_0})^k\). The FFAG procedure allows overlapping of fringe fields of neighboring dipoles, thus simulating in some sort the field in a dipole N-tuple - as for instance in an FFAG doublet or triplet. A detailed application, with five dipoles, can be found in Ref. [44]. This is done in the way described below.The dimensioning of the magnet is defined by :
AT : total angular aperture
RM : mean radius used for the positioning of field boundaries
For each one of the N = 1 to (maximum) 5 dipoles of the N-tuple, the two effective field boundaries (entrance and exit EFBs) from which the dipole field is drawn are defined from geometric boundaries, the shape and position of which are determined by the following parameters (in the same manner as in
DIPOLE,DIPOLE-M) (see Fig. 11-A page 98, and Fig. 31):\(ACN_i\) : arbitrary inner angle, used for EFBs positioning
ω : azimuth of an EFB with respect to ACN
θ : angle of an EFB with respect to its azimuth (wedge angle)
R1, R2 : radius of curvature of an EFB
U1, U2 : extent of the linear part of an EFB
Calculation of the Field From a Single Dipole
The magnetic field is calculated in polar coordinates. At all (R, θ) in the median plane (z = 0), the magnetic field due a single one (index i) of the dipoles of a N-tuple FFAG magnet is written $$B_{Z_i}(R, θ) = B_{Z_{0,i}} F_i(R, θ) (R/RM)^{K_i}$$ wherein \(B_{Z_{0,i}}\) is a reference field, at reference radius \(RM_i\), whereas F(R,θ) is calculated as described below.
Calculation of \(F_i(R, θ)\)
The fringe field coefficient \(F_i(R, θ)\) associated with a dipole is computed as in the procedure
DIPOLES(eq. 6.4.16), including (rigorously if the interpolation method is used, see page 125, or to order zero if the analytic method is used, see page 125) radial dependence of the gap size $$g(R) = g_0 (RM/R)^κ (6.4.19) $$ so to simulate the effect of gap shaping on \(B_{Z_i}(R,θ)|_R\) field fall-off, over the all radial extent of a scaling FFAG dipole (with normally - but not necessarily in practice - κ ≈ Ki).Calculation of the Field Resulting From All N Dipoles
For the rest, namely, calculation of the full field at particle position from the N dipoles, analytical calculation or numerical interpolation of the mid-plane field derivatives, extrapolation off median plane, etc., things are performed exactly as in the case of the
DIPOLESprocedure (see page 125).Sharp Edge
Sharp edge field fall-off at a field boundary can only be simulated if the following conditions are fulfilled :
Entrance (resp. exit) field boundary coincides with entrance (resp. exit) dipole limit (it means in particular see Fig. 11, \(ω^+ = ACENT\) (resp. \(ω^- = −(AT − ACENT\))), together with θ = 0 at entrance (resp. exit) EFBs)
Analytical method for calculation of the mid-plane field derivatives is used.
Command attributes
-
LABEL1='' Primary label for the Zgoubi command (default: auto-generated hash).
- Type
str
-
LABEL2='' Secondary label for the Zgoubi command.
- Type
str
-
HEIGHT='20 centimeter' Height of the magnet (distance between poles), used by plotting functions.
- Type
Quantity
-
POLE_WIDTH='150 centimeter' Pole width (used for plotting only).
- Type
Quantity
-
PIPE_THICKNESS='2 centimeter' Thickness of the pipe, used by plotting functions.
- Type
Quantity
-
PIPE_COLOR='grey' Color of the pipe, used by plotting functions.
- Type
str
-
REFERENCE_FIELD_COMPONENT='BZ' Orientation of the reference field (used by field maps)
- Type
str
-
KINEMATICS='None' A kinematics object.
- Type
NoneType
-
APERTURE_LEFT='10 centimeter' Aperture size of the magnet, left side (used for plotting only).
- Type
Quantity
-
APERTURE_RIGHT='10 centimeter' Aperture size of the magnet, right side (used for plotting only).
- Type
Quantity
-
APERTURE_TOP='10 centimeter' Aperture size of the magnet, top side (used for plotting only).
- Type
Quantity
-
APERTURE_BOTTOM='10 centimeter' Aperture size of the magnet, bottom side (used for plotting only).
- Type
Quantity
-
IL='0' Print field and coordinates along trajectories
- Type
int
-
N='1' Number of dipoles in the FFAG N -tuple (maximum 5)
- Type
int
-
AT='0.0 degree' Total angular extent of the N dipoles
- Type
Quantity
-
RM='0.0 centimeter' Reference radius: mean radius used for the positioning of field boundaries
- Type
Quantity
-
ACN='[0.0 0.0 0.0 0.0 0.0] degree' Azimuth for dipole positioning
- Type
Quantity
-
DRM='[0.0 0.0 0.0 0.0 0.0] centimeter' Offset for the reference radius of each dipole RM_i = RM + DRM
- Type
Quantity
-
BZ0='[0.0 0.0 0.0 0.0 0.0] kilogauss' Field of each dipole
- Type
Quantity
-
K='[0.0, 0.0, 0.0, 0.0, 0.0]' Field index for each dipole
- Type
list
-
G0_E='[1e-08 1e-08 1e-08 1e-08 1e-08] centimeter' Reference gaps for the entrance fringe fields of each dipole.
- Type
Quantity
-
K_E='[0, 0, 0, 0, 0]' Fringe field parameter kappa
- Type
list
-
C0_E='[0, 0, 0, 0, 0]' Fringe field coefficient C0
- Type
list
-
C1_E='[1, 1, 1, 1, 1]' Fringe field coefficient C1
- Type
list
-
C2_E='[0, 0, 0, 0, 0]' Fringe field coefficient C2
- Type
list
-
C3_E='[0, 0, 0, 0, 0]' Fringe field coefficient C3
- Type
list
-
C4_E='[0, 0, 0, 0, 0]' Fringe field coefficient C4
- Type
list
-
C5_E='[0, 0, 0, 0, 0]' Fringe field coefficient C5
- Type
list
-
SHIFT_E='[0.0 0.0 0.0 0.0 0.0] centimeter' Shift of the EFB
- Type
Quantity
-
OMEGA_E='[0.0 0.0 0.0 0.0 0.0] degree' - Type
Quantity
-
THETA_E='[0.0 0.0 0.0 0.0 0.0] degree' Entrance face wedge angle
- Type
Quantity
-
R1_E='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' Entrance EFB radius
- Type
Quantity
-
U1_E='[-1000000000.0 -1000000000.0 -1000000000.0 -1000000000.0 -1000000000.0] centimeter' Entrance EFB linear extent
- Type
Quantity
-
U2_E='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' Entrance EFB linear extent
- Type
Quantity
-
R2_E='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' Entrance EFB radius
- Type
Quantity
-
G0_S='[1e-08 1e-08 1e-08 1e-08 1e-08] centimeter' Reference gaps for the exit fringe fields of each dipole.
- Type
Quantity
-
K_S='[0, 0, 0, 0, 0]' Fringe field parameter kappa
- Type
list
-
C0_S='[0, 0, 0, 0, 0]' Fringe field coefficient C0
- Type
list
-
C1_S='[1, 1, 1, 1, 1]' Fringe field coefficient C1
- Type
list
-
C2_S='[0, 0, 0, 0, 0]' Fringe field coefficient C2
- Type
list
-
C3_S='[0, 0, 0, 0, 0]' Fringe field coefficient C3
- Type
list
-
C4_S='[0, 0, 0, 0, 0]' Fringe field coefficient C4
- Type
list
-
C5_S='[0, 0, 0, 0, 0]' Fringe field coefficient C5
- Type
list
-
SHIFT_S='[0.0 0.0 0.0 0.0 0.0] centimeter' Shift of the EFB
- Type
Quantity
-
OMEGA_S='[0.0 0.0 0.0 0.0 0.0] degree' - Type
Quantity
-
THETA_S='[0.0 0.0 0.0 0.0 0.0] degree' Entrance face wedge angle
- Type
Quantity
-
R1_S='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' Exit EFB radius
- Type
Quantity
-
U1_S='[-1000000000.0 -1000000000.0 -1000000000.0 -1000000000.0 -1000000000.0] centimeter' Exit EFB linear extent
- Type
Quantity
-
U2_S='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' Exit EFB linear extent
- Type
Quantity
-
R2_S='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' Exit EFB radius
- Type
Quantity
-
G0_L='[0.0 0.0 0.0 0.0 0.0] centimeter' UNUSED Reference gaps for the lateral fringe fields of each dipole.
- Type
Quantity
-
K_L='[-1, -1, -1, -1, -1]' UNUSED Fringe field parameter kappa
- Type
list
-
C0_L='[0, 0, 0, 0, 0]' UNUSED Fringe field coefficient C0
- Type
list
-
C1_L='[0, 0, 0, 0, 0]' UNUSED Fringe field coefficient C1
- Type
list
-
C2_L='[0, 0, 0, 0, 0]' UNUSED Fringe field coefficient C2
- Type
list
-
C3_L='[0, 0, 0, 0, 0]' UNUSED Fringe field coefficient C3
- Type
list
-
C4_L='[0, 0, 0, 0, 0]' UNUSED Fringe field coefficient C4
- Type
list
-
C5_L='[0, 0, 0, 0, 0]' UNUSED Fringe field coefficient C5
- Type
list
-
SHIFT_L='[0.0 0.0 0.0 0.0 0.0] centimeter' UNUSED Shift of the EFB
- Type
Quantity
-
OMEGA_L='[0.0 0.0 0.0 0.0 0.0] degree' UNUSED
- Type
Quantity
-
THETA_L='[0.0 0.0 0.0 0.0 0.0] degree' UNUSED Entrance face wedge angle
- Type
Quantity
-
R1_L='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' UNUSED Lateral EFB radius
- Type
Quantity
-
U1_L='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' UNUSED Lateral EFB linear extent
- Type
Quantity
-
U2_L='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' UNUSED Lateral EFB linear extent
- Type
Quantity
-
R2_L='[1000000000.0 1000000000.0 1000000000.0 1000000000.0 1000000000.0] centimeter' UNUSED Lateral EFB radius
- Type
Quantity
-
KIRD='2' Analytical computation (KIRD = 0) or numerical interpolation (KIRD = 2,4, 25) of field derivatives
- Type
int
-
RESOL='2' - Type
int
-
XPAS='1.0 millimeter' Integration step
- Type
Quantity
-
KPOS='2' - Type
int
-
RE='0.0 centimeter' - Type
Quantity
-
TE='0.0 radian' - Type
Quantity
-
RS='0.0 centimeter' - Type
Quantity
-
TS='0.0 radian' - Type
Quantity
-
DP='0.0' - Type
float
Default initializer for all Commands.
Attributes Summary
Keyword of the command used for the Zgoubi input data.
Parameters of the command, with their default value, their description and optinally an index used by other commands (e.g.
Methods Summary
post_init(**kwargs)- param **kwargs
Attributes Documentation
-
KEYWORD: str = 'FFAG'¶ Keyword of the command used for the Zgoubi input data.
-
PARAMETERS: dict = {'ACN': (<Quantity([0. 0. 0. 0. 0.], 'degree')>, 'Azimuth for dipole positioning', 5), 'APERTURE_BOTTOM': (<Quantity(10, 'centimeter')>, 'Aperture size of the magnet, bottom side (used for plotting only).'), 'APERTURE_LEFT': (<Quantity(10, 'centimeter')>, 'Aperture size of the magnet, left side (used for plotting only).'), 'APERTURE_RIGHT': (<Quantity(10, 'centimeter')>, 'Aperture size of the magnet, right side (used for plotting only).'), 'APERTURE_TOP': (<Quantity(10, 'centimeter')>, 'Aperture size of the magnet, top side (used for plotting only).'), 'AT': (<Quantity(0.0, 'degree')>, 'Total angular extent of the N dipoles', 3), 'BZ0': (<Quantity([0. 0. 0. 0. 0.], 'kilogauss')>, 'Field of each dipole', 7), 'C0_E': ([0, 0, 0, 0, 0], 'Fringe field coefficient C0', 12), 'C0_L': ([0, 0, 0, 0, 0], 'UNUSED Fringe field coefficient C0', 44), 'C0_S': ([0, 0, 0, 0, 0], 'Fringe field coefficient C0', 28), 'C1_E': ([1, 1, 1, 1, 1], 'Fringe field coefficient C1', 13), 'C1_L': ([0, 0, 0, 0, 0], 'UNUSED Fringe field coefficient C1', 45), 'C1_S': ([1, 1, 1, 1, 1], 'Fringe field coefficient C1', 29), 'C2_E': ([0, 0, 0, 0, 0], 'Fringe field coefficient C2', 14), 'C2_L': ([0, 0, 0, 0, 0], 'UNUSED Fringe field coefficient C2', 46), 'C2_S': ([0, 0, 0, 0, 0], 'Fringe field coefficient C2', 30), 'C3_E': ([0, 0, 0, 0, 0], 'Fringe field coefficient C3', 15), 'C3_L': ([0, 0, 0, 0, 0], 'UNUSED Fringe field coefficient C3', 47), 'C3_S': ([0, 0, 0, 0, 0], 'Fringe field coefficient C3', 31), 'C4_E': ([0, 0, 0, 0, 0], 'Fringe field coefficient C4', 16), 'C4_L': ([0, 0, 0, 0, 0], 'UNUSED Fringe field coefficient C4', 48), 'C4_S': ([0, 0, 0, 0, 0], 'Fringe field coefficient C4', 32), 'C5_E': ([0, 0, 0, 0, 0], 'Fringe field coefficient C5', 16), 'C5_L': ([0, 0, 0, 0, 0], 'UNUSED Fringe field coefficient C5', 49), 'C5_S': ([0, 0, 0, 0, 0], 'Fringe field coefficient C5', 33), 'COLOR': ('#4169E1',), 'DP': (0.0, '', 61), 'DRM': (<Quantity([0. 0. 0. 0. 0.], 'centimeter')>, 'Offset for the reference radius of each dipole RM_i = RM + DRM', 6), 'G0_E': (<Quantity([1.e-08 1.e-08 1.e-08 1.e-08 1.e-08], 'centimeter')>, 'Reference gaps for the entrance fringe fields of each dipole.', 9), 'G0_L': (<Quantity([0. 0. 0. 0. 0.], 'centimeter')>, 'UNUSED Reference gaps for the lateral fringe fields of each dipole.', 41), 'G0_S': (<Quantity([1.e-08 1.e-08 1.e-08 1.e-08 1.e-08], 'centimeter')>, 'Reference gaps for the exit fringe fields of each dipole.', 25), 'HEIGHT': (<Quantity(20, 'centimeter')>, 'Height of the magnet (distance between poles), used by plotting functions.'), 'IL': (0, 'Print field and coordinates along trajectories', 1), 'K': ([0.0, 0.0, 0.0, 0.0, 0.0], 'Field index for each dipole', 8), 'KINEMATICS': (None, 'A kinematics object.'), 'KIRD': (2, 'Analytical computation (KIRD = 0) or numerical interpolation (KIRD = 2,4, 25) of field derivatives', 57), 'KPOS': (2, '', 60), 'K_E': ([0, 0, 0, 0, 0], 'Fringe field parameter kappa', 10), 'K_L': ([-1, -1, -1, -1, -1], 'UNUSED Fringe field parameter kappa', 42), 'K_S': ([0, 0, 0, 0, 0], 'Fringe field parameter kappa', 26), 'LABEL1': ('', 'Primary label for the Zgoubi command (default: auto-generated hash).'), 'LABEL2': ('', 'Secondary label for the Zgoubi command.'), 'N': (1, 'Number of dipoles in the FFAG N -tuple (maximum 5)', 2), 'OMEGA_E': (<Quantity([0. 0. 0. 0. 0.], 'degree')>, '', 19), 'OMEGA_L': (<Quantity([0. 0. 0. 0. 0.], 'degree')>, 'UNUSED ', 51), 'OMEGA_S': (<Quantity([0. 0. 0. 0. 0.], 'degree')>, '', 35), 'PIPE_COLOR': ('grey', 'Color of the pipe, used by plotting functions.'), 'PIPE_THICKNESS': (<Quantity(2, 'centimeter')>, 'Thickness of the pipe, used by plotting functions.'), 'POLE_WIDTH': (<Quantity(150, 'centimeter')>, 'Pole width (used for plotting only).'), 'R1_E': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'Entrance EFB radius', 21), 'R1_L': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'UNUSED Lateral EFB radius', 53), 'R1_S': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'Exit EFB radius', 37), 'R2_E': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'Entrance EFB radius', 24), 'R2_L': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'UNUSED Lateral EFB radius', 56), 'R2_S': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'Exit EFB radius', 40), 'RE': (<Quantity(0.0, 'centimeter')>, '', 61), 'REFERENCE_FIELD_COMPONENT': ('BZ', 'Orientation of the reference field (used by field maps)'), 'RESOL': (2, '', 58), 'RM': (<Quantity(0.0, 'centimeter')>, 'Reference radius: mean radius used for the positioning of field boundaries', 4), 'RS': (<Quantity(0.0, 'centimeter')>, '', 63), 'SHIFT_E': (<Quantity([0. 0. 0. 0. 0.], 'centimeter')>, 'Shift of the EFB', 18), 'SHIFT_L': (<Quantity([0. 0. 0. 0. 0.], 'centimeter')>, 'UNUSED Shift of the EFB', 50), 'SHIFT_S': (<Quantity([0. 0. 0. 0. 0.], 'centimeter')>, 'Shift of the EFB', 34), 'TE': (<Quantity(0.0, 'radian')>, '', 62), 'THETA_E': (<Quantity([0. 0. 0. 0. 0.], 'degree')>, 'Entrance face wedge angle', 20), 'THETA_L': (<Quantity([0. 0. 0. 0. 0.], 'degree')>, 'UNUSED Entrance face wedge angle', 52), 'THETA_S': (<Quantity([0. 0. 0. 0. 0.], 'degree')>, 'Entrance face wedge angle', 36), 'TS': (<Quantity(0.0, 'radian')>, '', 64), 'U1_E': (<Quantity([-1.e+09 -1.e+09 -1.e+09 -1.e+09 -1.e+09], 'centimeter')>, 'Entrance EFB linear extent', 22), 'U1_L': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'UNUSED Lateral EFB linear extent', 54), 'U1_S': (<Quantity([-1.e+09 -1.e+09 -1.e+09 -1.e+09 -1.e+09], 'centimeter')>, 'Exit EFB linear extent', 38), 'U2_E': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'Entrance EFB linear extent', 23), 'U2_L': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'UNUSED Lateral EFB linear extent', 55), 'U2_S': (<Quantity([1.e+09 1.e+09 1.e+09 1.e+09 1.e+09], 'centimeter')>, 'Exit EFB linear extent', 39), 'XPAS': (<Quantity(1.0, 'millimeter')>, 'Integration step', 59)}¶ Parameters of the command, with their default value, their description and optinally an index used by other commands (e.g. fit).
Methods Documentation