Lattice Elements

General Syntax for Defining a Lattice Element

<lattice_name>: <element_type>, <param1> = <val1>, <param2> = <val2>, ...

Example:

d1: drift, l = 1.2   ! 1.2 m drift space called "d1"
mk: marker           ! Marker element called "mk".

Notes:

• Marker elements have zero length.

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Quadrupole Elements

Example:

beginning[beta_a] = 10.     ! m  a-mode beta function
beginning[beta_b] = 10.     ! m  b-mode beta function
parameter[p0c] = 1e6        ! Set reference momentum * c_light in eV.
parameter[geometry] = open  ! or closed

q1: quad, l = 0.6, k1 = 0.14
q2: quad, l = 0.6, b1_gradient = parameter[p0c] * q1[k1] / c_light

lat: line =	(q1, q2)
use, lat

Put this lattice into a file called "quad.bmad" and run Tao:

> tao -lat quad.bmad

Tao> show ele 2
 Element #                2
 Element Name: Q2
 Key: Quadrupole
 S_start, S:    0.600000,    1.200000
 Ref_time:  4.495094E-09

 Attribute values [Only non-zero/non-default values shown]:
    1   L                            =  6.0000000E-01 m
    4   K1                           =  1.4000000E-01 1/m^2    ! Same as Q1 !!!
   13   SPIN_FRINGE_ON               =  T (1)
   31   L_HARD_EDGE                  =  6.0000000E-01 m
   45   B1_GRADIENT                  =  4.6698973E-04 T/m
   47   PTC_CANONICAL_COORDS         =  1.0000000E+00
   50   DELTA_REF_TIME               =  2.2475468E-09 sec
   53   P0C                          =  1.0000000E+06 eV            BETA            =  0.890475155
   54   E_TOT                        =  1.1229960E+06 eV            GAMMA           =  2.1976483E+00
... etc...
         FIELD_MASTER                 =  T

This illustrates that the quadrupole field gradient can be set using the normalized gradient k1 or the "unnormalized" field itself using b1_gradient.

Roughly, the angular deflection an on-energy particle with offset delta_x from the center line feels going through the quad is

delta x' = k1 * L * delta_x

Notes:

• Positive k1 gives focusing in the horizontal plane and defocusing in the vertical plane.
• If k1 is specified, Bmad will compute b1_gradient and vice versa.
• To tilt a quadrupole use the tilt parameter.

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Bend Elements

If the e1 and e2 face angles are zero, rbends are "rectangular" shaped bending magnets and sbends are "sector" shaped bending magnets.

Main Bend parameters are:

angle	Bending angle α (radians).
rho	Bending radius (m).
g	Bending strength = 1 / rho.
l	length of element. Note: For an rbend, l is the chord length!
e1, e2	Face rotation angles (radians).

Example:

b: sbend, l = 3.2, angle = 90*deg, e1 = b[angle]/2, e2 = b[angle]/2

Notes:

• angle, rho, g and l are not all independent. You must specify two and only two (and not rho and g together) and Bmad will compute the other two.
• Internally, Bmad converts all rbends to sbends. Never search for rbends when running Tao. You will not find any.
• When an rbend is converted to an sbend, l -> l_chord.

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More Info

Bmad has many element types to choose from: