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Particle Beam Statistics Standard

This document defines the standard statistics available in ParticleGroup. Schema version: 1.0

See Statistics Schema for documentation on how to extend this standard.

Unit dimensions follow the openPMD unit system: (length, mass, time, current, temperature, amount, luminous intensity).

Contents

Phase Space Coordinates

Basic position and momentum coordinates in Cartesian space.

Label Symbol Units Description
x \(x\) m Horizontal position coordinate.
y \(y\) m Vertical position coordinate.
z \(z\) m Longitudinal position coordinate.
px \(p_x\) eV/c Horizontal momentum component.
py \(p_y\) eV/c Vertical momentum component.
pz \(p_z\) eV/c Longitudinal momentum component.

Time Coordinate

Time-related quantities.

Label Symbol Units Description
t \(t\) s Time coordinate of the particle.
z/c \(z/c\) s Position expressed as time (z divided by speed of light).

Relativistic Quantities

Relativistic energy, momentum, and velocity factors.

Label Symbol Units Description
p \(p\) eV/c Total momentum magnitude.
energy \(E\) eV Total relativistic energy.
kinetic_energy \(E_\text{kinetic}\) eV Kinetic energy (total energy minus rest mass energy).
mass \(m\) eV Rest mass energy of the particle species.
gamma \(\gamma\) 1 Relativistic Lorentz factor.
beta \(\beta\) 1 Relativistic velocity divided by speed of light.
beta_x \(\beta_x\) 1 Horizontal component of relativistic velocity / c.
beta_y \(\beta_y\) 1 Vertical component of relativistic velocity / c.
beta_z \(\beta_z\) 1 Longitudinal component of relativistic velocity / c.
higher_order_energy \(E_{(2)}\) eV Energy with a polynomial fit (default quadratic) in z or t subtracted. Used t...
higher_order_energy_spread \(\sigma_{E_{(2)}}\) eV Standard deviation of higher_order_energy.

Transverse Slopes

Angular divergence quantities.

Label Symbol Units Description
xp \(x'\) rad Horizontal divergence angle (slope dx/dz).
yp \(y'\) rad Vertical divergence angle (slope dy/dz).

Polar/Cylindrical Coordinates

Cylindrical coordinate representations.

Label Symbol Units Description
r \(r\) m Radial distance from the z-axis in cylindrical coordinates.
theta \(\theta\) rad Azimuthal angle in the x-y plane.
pr \(p_r\) eV/c Radial momentum component in cylindrical coordinates.
ptheta \(p_{\theta}\) eV/c Azimuthal momentum component in cylindrical coordinates.
Lz \(L_z\) m*eV/c Angular momentum about the z-axis.

Normalized Coordinates

Courant-Snyder normalized phase space coordinates and amplitudes.

Label Symbol Units Description
x_bar \(\overline{x}\) sqrt(m) Courant-Snyder normalized horizontal position coordinate. Computed from the b...
px_bar \(\overline{p_x}\) sqrt(m) Courant-Snyder normalized horizontal momentum coordinate. Computed from the b...
y_bar \(\overline{y}\) sqrt(m) Courant-Snyder normalized vertical position coordinate. Computed from the bea...
py_bar \(\overline{p_y}\) sqrt(m) Courant-Snyder normalized vertical momentum coordinate. Computed from the bea...
Jx \(J_x\) m Normalized action (amplitude) in the horizontal plane. The average equals the...
Jy \(J_y\) m Normalized action (amplitude) in the vertical plane. The average equals the n...

Emittance

Beam emittance quantities measuring phase space volume.

Label Symbol Units Description
norm_emit_x \(\epsilon_{n,x}\) m Normalized RMS emittance in the horizontal plane. Invariant under linear tran...
norm_emit_y \(\epsilon_{n,y}\) m Normalized RMS emittance in the vertical plane. Invariant under linear transp...
norm_emit_4d \(\epsilon_{4D}\) m^2 4D normalized emittance in transverse (x-y) phase space. Square root of deter...

Twiss Parameters

Courant-Snyder (Twiss) lattice functions and dispersion.

Label Symbol Units Description
twiss_alpha_x \(\alpha_x\) 1 Courant-Snyder alpha parameter in horizontal plane.
twiss_beta_x \(\beta_x\) m Courant-Snyder beta function in horizontal plane.
twiss_gamma_x \(\gamma_x\) 1/m Courant-Snyder gamma parameter in horizontal plane.
twiss_emit_x \(\epsilon_x\) m Geometric RMS emittance in horizontal plane.
twiss_norm_emit_x \(\epsilon_{n,x}\) m Normalized emittance from Twiss calculation in horizontal plane.
twiss_eta_x \(\eta_x\) m Horizontal dispersion function.
twiss_etap_x \(\eta'_x\) 1 Derivative of horizontal dispersion function.
twiss_alpha_y \(\alpha_y\) 1 Courant-Snyder alpha parameter in vertical plane.
twiss_beta_y \(\beta_y\) m Courant-Snyder beta function in vertical plane.
twiss_gamma_y \(\gamma_y\) 1/m Courant-Snyder gamma parameter in vertical plane.
twiss_emit_y \(\epsilon_y\) m Geometric RMS emittance in vertical plane.
twiss_norm_emit_y \(\epsilon_{n,y}\) m Normalized emittance from Twiss calculation in vertical plane.
twiss_eta_y \(\eta_y\) m Vertical dispersion function.
twiss_etap_y \(\eta'_y\) 1 Derivative of vertical dispersion function.

Beam Properties

Integrated beam properties like charge, current, and bunching.

Label Symbol Units Description
charge \(Q\) C Total beam charge (sum of particle weights).
weight \(w\) C Macro-particle charge weight used for statistical calculations.
species_charge \(q\) C Elementary charge of the particle species.
average_current \(I_{av}\) A Simple average current computed as total charge divided by bunch length in time.
bunching \(b(\lambda)\) 1 Complex bunching parameter at a given wavelength. Magnitude indicates modulat...

Particle Properties

Individual particle properties and counts.

Label Symbol Units Description
n_particle \(N\) 1 Total number of macro-particles in the group.
n_alive \(N_{alive}\) 1 Number of particles with status equal to 1 (alive/active).
n_dead \(N_{dead}\) 1 Number of particles with status not equal to 1 (lost/inactive).
status \(\text{status}\) 1 Particle status flag. A value of 1 indicates an alive particle; other values ...
id \(\text{id}\) 1 Unique integer identifier for each particle.

Detailed Definitions

Phase Space Coordinates

x

Symbol: \(x\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Horizontal position coordinate.

Reference: openPMD-beamphysics standard

y

Symbol: \(y\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Vertical position coordinate.

Reference: openPMD-beamphysics standard

z

Symbol: \(z\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Longitudinal position coordinate.

Reference: openPMD-beamphysics standard

px

Symbol: \(p_x\)

Units: eV/c

unitSI: 5.344285992678308e-28

unitDimension: (1, 1, -1, 0, 0, 0, 0)

Horizontal momentum component.

Reference: openPMD-beamphysics standard

py

Symbol: \(p_y\)

Units: eV/c

unitSI: 5.344285992678308e-28

unitDimension: (1, 1, -1, 0, 0, 0, 0)

Vertical momentum component.

Reference: openPMD-beamphysics standard

pz

Symbol: \(p_z\)

Units: eV/c

unitSI: 5.344285992678308e-28

unitDimension: (1, 1, -1, 0, 0, 0, 0)

Longitudinal momentum component.

Reference: openPMD-beamphysics standard

Time Coordinate

t

Symbol: \(t\)

Units: s

unitSI: 1

unitDimension: (0, 0, 1, 0, 0, 0, 0)

Time coordinate of the particle.

Reference: openPMD-beamphysics standard

z/c

Symbol: \(z/c\)

Units: s

unitSI: 1

unitDimension: (0, 0, 1, 0, 0, 0, 0)

Position expressed as time (z divided by speed of light).

Reference: openPMD-beamphysics standard

Relativistic Quantities

p

Symbol: \(p\)

Units: eV/c

unitSI: 5.344285992678308e-28

unitDimension: (1, 1, -1, 0, 0, 0, 0)

Total momentum magnitude.

Formula:

\[p = \sqrt{p_x^2 + p_y^2 + p_z^2}\]

Reference: openPMD-beamphysics standard

energy

Symbol: \(E\)

Units: eV

unitSI: 1.602176634e-19

unitDimension: (2, 1, -2, 0, 0, 0, 0)

Total relativistic energy.

Formula:

\[E = \sqrt{p^2 c^2 + m^2 c^4}\]

Reference: openPMD-beamphysics standard

kinetic_energy

Symbol: \(E_\text{kinetic}\)

Units: eV

unitSI: 1.602176634e-19

unitDimension: (2, 1, -2, 0, 0, 0, 0)

Kinetic energy (total energy minus rest mass energy).

Formula:

\[E_\text{kinetic} = E - mc^2\]

Reference: openPMD-beamphysics standard

mass

Symbol: \(m\)

Units: eV

unitSI: 1.602176634e-19

unitDimension: (2, 1, -2, 0, 0, 0, 0)

Rest mass energy of the particle species.

Reference: openPMD-beamphysics standard

gamma

Symbol: \(\gamma\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Relativistic Lorentz factor.

Formula:

\[\gamma = E / (mc^2)\]

Reference: openPMD-beamphysics standard

beta

Symbol: \(\beta\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Relativistic velocity divided by speed of light.

Formula:

\[\beta = p / E = v / c\]

Reference: openPMD-beamphysics standard

beta_x

Symbol: \(\beta_x\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Horizontal component of relativistic velocity / c.

Formula:

\[\beta_x = p_x / E\]

Reference: openPMD-beamphysics standard

beta_y

Symbol: \(\beta_y\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Vertical component of relativistic velocity / c.

Formula:

\[\beta_y = p_y / E\]

Reference: openPMD-beamphysics standard

beta_z

Symbol: \(\beta_z\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Longitudinal component of relativistic velocity / c.

Formula:

\[\beta_z = p_z / E\]

Reference: openPMD-beamphysics standard

higher_order_energy

Symbol: \(E_{(2)}\)

Units: eV

unitSI: 1.602176634e-19

unitDimension: (2, 1, -2, 0, 0, 0, 0)

Energy with a polynomial fit (default quadratic) in z or t subtracted. Used to isolate higher-order energy correlations.

Reference: openPMD-beamphysics standard

higher_order_energy_spread

Symbol: \(\sigma_{E_{(2)}}\)

Units: eV

unitSI: 1.602176634e-19

unitDimension: (2, 1, -2, 0, 0, 0, 0)

Standard deviation of higher_order_energy.

Formula:

\[\sigma_{E_{(2)}} = \text{std}(E_{(2)})\]

Reference: openPMD-beamphysics standard

Transverse Slopes

xp

Symbol: \(x'\)

Units: rad

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Horizontal divergence angle (slope dx/dz).

Formula:

\[x' = p_x / p_z\]

Reference: openPMD-beamphysics standard

yp

Symbol: \(y'\)

Units: rad

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Vertical divergence angle (slope dy/dz).

Formula:

\[y' = p_y / p_z\]

Reference: openPMD-beamphysics standard

Polar/Cylindrical Coordinates

r

Symbol: \(r\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Radial distance from the z-axis in cylindrical coordinates.

Formula:

\[r = \sqrt{x^2 + y^2}\]

Reference: openPMD-beamphysics standard

theta

Symbol: \(\theta\)

Units: rad

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Azimuthal angle in the x-y plane.

Formula:

\[\theta = \arctan(y/x)\]

Reference: openPMD-beamphysics standard

pr

Symbol: \(p_r\)

Units: eV/c

unitSI: 5.344285992678308e-28

unitDimension: (1, 1, -1, 0, 0, 0, 0)

Radial momentum component in cylindrical coordinates.

Formula:

\[p_r = p_x \cos\theta + p_y \sin\theta\]

Reference: openPMD-beamphysics standard

ptheta

Symbol: \(p_{\theta}\)

Units: eV/c

unitSI: 5.344285992678308e-28

unitDimension: (1, 1, -1, 0, 0, 0, 0)

Azimuthal momentum component in cylindrical coordinates.

Formula:

\[p_\theta = -p_x \sin\theta + p_y \cos\theta\]

Reference: openPMD-beamphysics standard

Lz

Symbol: \(L_z\)

Units: m*eV/c

unitSI: 5.344285992678308e-28

unitDimension: (2, 1, -1, 0, 0, 0, 0)

Angular momentum about the z-axis.

Formula:

\[L_z = x p_y - y p_x = r \cdot p_\theta\]

Reference: openPMD-beamphysics standard

Normalized Coordinates

x_bar

Symbol: \(\overline{x}\)

Units: sqrt(m)

unitSI: 1.0

unitDimension: (0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

Courant-Snyder normalized horizontal position coordinate. Computed from the beam's covariance matrix.

Formula:

\[\overline{x} = x / \sqrt{\beta_x}\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

px_bar

Symbol: \(\overline{p_x}\)

Units: sqrt(m)

unitSI: 1.0

unitDimension: (0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

Courant-Snyder normalized horizontal momentum coordinate. Computed from the beam's covariance matrix.

Formula:

\[\overline{p_x} = (\alpha_x x + \beta_x x') / \sqrt{\beta_x}\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

y_bar

Symbol: \(\overline{y}\)

Units: sqrt(m)

unitSI: 1.0

unitDimension: (0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

Courant-Snyder normalized vertical position coordinate. Computed from the beam's covariance matrix.

Formula:

\[\overline{y} = y / \sqrt{\beta_y}\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

py_bar

Symbol: \(\overline{p_y}\)

Units: sqrt(m)

unitSI: 1.0

unitDimension: (0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

Courant-Snyder normalized vertical momentum coordinate. Computed from the beam's covariance matrix.

Formula:

\[\overline{p_y} = (\alpha_y y + \beta_y y') / \sqrt{\beta_y}\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

Jx

Symbol: \(J_x\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Normalized action (amplitude) in the horizontal plane. The average equals the normalized emittance.

Formula:

\[J_x = (\overline{x}^2 + \overline{p_x}^2) / 2\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

Jy

Symbol: \(J_y\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Normalized action (amplitude) in the vertical plane. The average equals the normalized emittance.

Formula:

\[J_y = (\overline{y}^2 + \overline{p_y}^2) / 2\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

Emittance

norm_emit_x

Symbol: \(\epsilon_{n,x}\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Normalized RMS emittance in the horizontal plane. Invariant under linear transport for a relativistic beam.

Formula:

\[\epsilon_{n,x} = \frac{1}{mc} \sqrt{\langle x^2 \rangle \langle p_x^2 \rangle - \langle x p_x \rangle^2}\]

Reference: Wiedemann, Particle Accelerator Physics (Springer)

norm_emit_y

Symbol: \(\epsilon_{n,y}\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Normalized RMS emittance in the vertical plane. Invariant under linear transport for a relativistic beam.

Formula:

\[\epsilon_{n,y} = \frac{1}{mc} \sqrt{\langle y^2 \rangle \langle p_y^2 \rangle - \langle y p_y \rangle^2}\]

Reference: Wiedemann, Particle Accelerator Physics (Springer)

norm_emit_4d

Symbol: \(\epsilon_{4D}\)

Units: m^2

unitSI: 1.0

unitDimension: (2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

4D normalized emittance in transverse (x-y) phase space. Square root of determinant of 4x4 covariance matrix normalized by (mc)^2.

Formula:

\[\epsilon_{4D} = \frac{1}{(mc)^2} \sqrt{\det(\Sigma_{4 \times 4})}\]

Reference: Wiedemann, Particle Accelerator Physics (Springer)

Twiss Parameters

twiss_alpha_x

Symbol: \(\alpha_x\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Courant-Snyder alpha parameter in horizontal plane.

Formula:

\[\alpha_x = -\langle x, x' \rangle / \epsilon_x\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_beta_x

Symbol: \(\beta_x\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Courant-Snyder beta function in horizontal plane.

Formula:

\[\beta_x = \langle x^2 \rangle / \epsilon_x\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_gamma_x

Symbol: \(\gamma_x\)

Units: 1/m

unitSI: 1.0

unitDimension: (-1, 0, 0, 0, 0, 0, 0)

Courant-Snyder gamma parameter in horizontal plane.

Formula:

\[\gamma_x = \langle x'^2 \rangle / \epsilon_x = (1 + \alpha_x^2) / \beta_x\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_emit_x

Symbol: \(\epsilon_x\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Geometric RMS emittance in horizontal plane.

Formula:

\[\epsilon_x = \sqrt{\langle x^2 \rangle \langle x'^2 \rangle - \langle x x' \rangle^2}\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_norm_emit_x

Symbol: \(\epsilon_{n,x}\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Normalized emittance from Twiss calculation in horizontal plane.

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_eta_x

Symbol: \(\eta_x\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Horizontal dispersion function.

Formula:

\[\eta_x = \langle x \delta \rangle / \langle \delta^2 \rangle\]

Reference: Wiedemann, Particle Accelerator Physics (Springer)

twiss_etap_x

Symbol: \(\eta'_x\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Derivative of horizontal dispersion function.

Formula:

\[\eta'_x = \langle x' \delta \rangle / \langle \delta^2 \rangle\]

Reference: Wiedemann, Particle Accelerator Physics (Springer)

twiss_alpha_y

Symbol: \(\alpha_y\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Courant-Snyder alpha parameter in vertical plane.

Formula:

\[\alpha_y = -\langle y, y' \rangle / \epsilon_y\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_beta_y

Symbol: \(\beta_y\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Courant-Snyder beta function in vertical plane.

Formula:

\[\beta_y = \langle y^2 \rangle / \epsilon_y\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_gamma_y

Symbol: \(\gamma_y\)

Units: 1/m

unitSI: 1.0

unitDimension: (-1, 0, 0, 0, 0, 0, 0)

Courant-Snyder gamma parameter in vertical plane.

Formula:

\[\gamma_y = \langle y'^2 \rangle / \epsilon_y = (1 + \alpha_y^2) / \beta_y\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_emit_y

Symbol: \(\epsilon_y\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Geometric RMS emittance in vertical plane.

Formula:

\[\epsilon_y = \sqrt{\langle y^2 \rangle \langle y'^2 \rangle - \langle y y' \rangle^2}\]

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_norm_emit_y

Symbol: \(\epsilon_{n,y}\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Normalized emittance from Twiss calculation in vertical plane.

Reference: Courant & Snyder, Ann. Phys. 3, 1-48 (1958)

twiss_eta_y

Symbol: \(\eta_y\)

Units: m

unitSI: 1

unitDimension: (1, 0, 0, 0, 0, 0, 0)

Vertical dispersion function.

Formula:

\[\eta_y = \langle y \delta \rangle / \langle \delta^2 \rangle\]

Reference: Wiedemann, Particle Accelerator Physics (Springer)

twiss_etap_y

Symbol: \(\eta'_y\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Derivative of vertical dispersion function.

Formula:

\[\eta'_y = \langle y' \delta \rangle / \langle \delta^2 \rangle\]

Reference: Wiedemann, Particle Accelerator Physics (Springer)

Beam Properties

charge

Symbol: \(Q\)

Units: C

unitSI: 1

unitDimension: (0, 0, 1, 1, 0, 0, 0)

Total beam charge (sum of particle weights).

Formula:

\[Q = \sum_i w_i\]

Reference: openPMD-beamphysics standard

weight

Symbol: \(w\)

Units: C

unitSI: 1

unitDimension: (0, 0, 1, 1, 0, 0, 0)

Macro-particle charge weight used for statistical calculations.

Reference: openPMD-beamphysics standard

species_charge

Symbol: \(q\)

Units: C

unitSI: 1

unitDimension: (0, 0, 1, 1, 0, 0, 0)

Elementary charge of the particle species.

Reference: openPMD-beamphysics standard

average_current

Symbol: \(I_{av}\)

Units: A

unitSI: 1

unitDimension: (0, 0, 0, 1, 0, 0, 0)

Simple average current computed as total charge divided by bunch length in time.

Formula:

\[I_{av} = Q / \Delta t\]

Reference: openPMD-beamphysics standard

bunching

Symbol: \(b(\lambda)\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Complex bunching parameter at a given wavelength. Magnitude indicates modulation depth; phase indicates centroid position.

Formula:

\[b(\lambda) = \frac{\sum_i w_i e^{i k z_i}}{\sum_i w_i}, \quad k = 2\pi/\lambda\]

Reference: K.-J. Kim, NIM A 250 (1986)

Particle Properties

n_particle

Symbol: \(N\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Total number of macro-particles in the group.

Reference: openPMD-beamphysics standard

n_alive

Symbol: \(N_{alive}\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Number of particles with status equal to 1 (alive/active).

Reference: openPMD-beamphysics standard

n_dead

Symbol: \(N_{dead}\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Number of particles with status not equal to 1 (lost/inactive).

Reference: openPMD-beamphysics standard

status

Symbol: \(\text{status}\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Particle status flag. A value of 1 indicates an alive particle; other values indicate various loss conditions.

Reference: openPMD-beamphysics standard

id

Symbol: \(\text{id}\)

Units: 1

unitSI: 1

unitDimension: (0, 0, 0, 0, 0, 0, 0)

Unique integer identifier for each particle.

Reference: openPMD-beamphysics standard

Computed Statistics

The following prefixes can be applied to any base statistic label:

Prefix Example Description
sigma_ sigma_x Standard deviation \(\sigma\)
mean_ mean_x Weighted average \(\langle x \rangle\)
min_ min_x Minimum value
max_ max_x Maximum value
ptp_ ptp_x Peak-to-peak (max - min)
delta_ delta_x Deviation from mean \(x - \langle x \rangle\)
cov_X__Y cov_x__px Covariance \(\langle X, Y \rangle\)

See Computed Statistics for a complete enumeration of all computed statistics.