COMSOL 6.2 - Particle Beam

	For 2D axisymmetric models, always select the Include out-of-plane degrees of freedom check box in the physics interface Advanced Settings section when modeling particle beams, since the out-of-plane position and velocity are crucial in ensuring that the released beam has the specified emittance and other beam parameters.

Select a : (the default), , or . This option determines how the position of the center of the beam is computed. For 2D axisymmetric model components, an additional option is available, (the default).

For enter coordinates for the rc (SI unit: m). When is selected, the section is shown. Add at least one point to the selection to specify the center of the beam.

The section of the Particle Beam feature contains images indicating how the phase space ellipses are constructed for the different settings available. To enable this, use in the toolbar.

The distribution places particles uniformly on the surface of a hyperellipsoid in 4-dimensional phase space. In 3D, this results in a particle distribution which is uniform in physical space, that is, the distance between particles is roughly the same throughout the beam cross-section.

The distribution places particles uniformly inside the volume of a hyperellipsoid in 4-dimensional phase space. This yields a distribution in physical space in which particles are placed preferentially toward the center of the beam.

The distribution fills the volume of a hyperellipsoid with a normal distribution density profile in 4-dimensional phase space. Similar to the and distributions, particles are preferentially placed closer to the center of the beam, although in this case, some particles can be placed a significant distance from the center

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In 3D, select a : (the default) or . If is selected, two different sets of beam parameters, such as emittance and Twiss parameters, can be specified for the two transverse directions. If is selected, the same beam parameters are used for both transverse directions.

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Select a : (the default) or . means that the semimajor and semiminor axes of the phase space ellipses are parallel to the phase space coordinate axis. For a beam that is not subjected to any forces, means that the beam is released at the location of the beam waist. allows the phase space ellipse to be rotated about its centroid.

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Select a : (the default) or . Twiss parameters are generally favored by accelerator physicists, as they provide a standard method of defining the geometric properties of the phase space ellipse. is often favored by spectrometer designers, as it allows the dimensions of the phase space ellipse and rotation angle to be specified directly.

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In some cases it is possible to specify the B (SI unit: A/m2) instead of emittance. The default value is 1 mA/m2. The beam emittance is then computed from the brightness and the specified . It is possible to enter a value or expression for the brightness of the beam if the following conditions are met:

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For 3D components, when the is set to , it is possible to specify different phase space distributions in two orthogonal transverse directions. To decide how these transverse directions are oriented, select a : or . When is selected, the section is shown. Add an edge to this selection to define the coordinate system with respect to which the beam emittance and Twiss parameters are defined. Quantities with subscript 1 (εrms,1, β1, and so on) are used to determine the distributions of the position and velocity components parallel to the selected edge. Quantities with subscript 2 correspond to the position and velocity components perpendicular to the selected edge and to the direction of beam propagation. If is selected, enter components of the t1 (dimensionless) directly. The default is the positive y direction.

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The β (SI unit: m). The default value is 1 m. The product of this and the emittance give an indication of the transverse size of the particle beam. For a given value of the beam emittance, increasing β causes the particle distribution in transverse position space to be broadened and the distribution in transverse velocity space to be tightened.

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The εrms (SI unit: m). The default is 1 mm. The emittance is a measure of the average spread of the particles in phase space. Qualitatively, a larger emittance means that the area occupied by the distribution of particles in phase space is larger.

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The B (SI unit: A/m2). The default is 1 mA/m2. For symmetric beams the brightness can used instead of specifying the emittance. This option is only available when a certain combination of settings are applied, as explained in the previous list.

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The α (dimensionless). The default is 0. When this value is nonzero, the phase space ellipse becomes rotated about the position-velocity axis. When is selected from the list, α = 0. The remaining Twiss parameter γ (SI unit: 1/m) is not specified because it is derived from α and β.

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The xm' (dimensionless). The default is 0.04. Larger values indicate that the particles will have higher velocities in the transverse direction with respect to the longitudinal direction.

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The θ (SI unit: rad). The default is 0. This rotates the phase space ellipse about the position-velocity axis.

Table 4-1: summary of initial transverse velocity options.
Sampling	orientation	transverse velocity specification	image	available input
KV	Upright	Twiss		β, εrms β, B
Waterbag	Upright	Twiss		β, εrms β, B
Parabolic	Upright	Twiss		β, εrms β, B
Gaussian	Upright	Twiss		β, εrms β, B
KV	Not upright	Twiss		β, εrms, α β, B, α
Waterbag	Not upright	Twiss		β, εrms, α β, B, α
Parabolic	Not upright	Twiss		β, εrms, α β, B, α
Gaussian	Not upright	Twiss		β, εrms, α β, B, α
KV	Upright	Dimensions		xm, xm’
Waterbag	Upright	Dimensions		xm, xm’
Parabolic	Upright	Dimensions		xm, xm’
Gaussian	Upright	Dimensions		xm, xm’
KV	Not upright	Dimensions		xm, xm’, θ
Waterbag	Not upright	Dimensions		xm, xm’, θ
Parabolic	Not upright	Dimensions		xm, xm’, θ
Gaussian	Not upright	Dimensions		xm, xm’, θ

Select a : (the default) or . This determines the physical quantity of the remaining inputs in this section, which are used to initialize the longitudinal component of the particle velocity. Select a : (the default), , , or . The following options are available.

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For , enter either a Em (SI unit: J), default 1 eV and a σ (SI unit: J), default 0.1 eV, or a Vm (SI unit: m/s), default 1 m/s and σ (SI unit: m/s), default 0.1 m/s. In both cases, also enter the . The default is 1, and this option determines the number of particles released for each initial position, meaning this value multiplies the total number of particles released. The longitudinal component of the velocity is sampled from a normal distribution, meaning that roughly 68% of the particles will have an initial velocity within one standard deviation, and 95% within two standard deviations.

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For , enter either a Emin (SI unit: J), default 1 eV and a Emax (SI unit: J), default 2 eV, or a Vmin (SI unit: m/s), default 1 m/s and Vmax (SI unit: m/s), default 2 m/s. In both cases, also enter the . The default is 1, and this option determines the number of particles released for each initial position, meaning this value multiplies the total number of particles released. The uniform distribution will always include the minimum and maximum velocity or energy values if the is greater than 1. If the is 1, the velocity magnitude is simply the mean of the minimum and maximum values.

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For , enter either a list of (SI unit: J) or a list of (SI unit: m/s). The length of this list determines how many particles are released per initial position.

Select the check box to reverse the longitudinal direction of the released particles. This is useful when the feature selection is an interior boundary, and the normal direction is ambiguous. The direction of beam propagation is indicated by arrows on the selected boundaries in the Graphics window.