Energy to Beta

The pyamtrack.converters.beta_from_energy function calculates the relativistic speed (beta) of a particle based on its energy per nucleon.

Function Purpose

The pyamtrack.converters.beta_from_energy function computes the relative speed of a particle (beta = v/c), where v is the particle's velocity and c is the speed of light.

Input Parameters

• input: The energy of the particle per nucleon in MeV/u. The function accepts the following types:
  • A single value as a float or int.
  • A numpy.ndarray of energy values.
  • A Python list of energy values.

Output

• The function returns the calculated beta value(s) as:
  • A float for a single input value.
  • A numpy.ndarray for a NumPy array input.
  • A Python list for a list input.

Notes

• The input energy must be non-negative. Negative energy values are invalid and will cause np.nan to be returned.
• The function supports both scalar and vectorized operations, making it efficient for batch calculations.

Example Usage

Single Value Input

import pyamtrack

energy = 150.0  # MeV/u
beta = pyamtrack.converters.beta_from_energy(energy)
print(f"Beta: {beta}")

NumPy Array Input

import pyamtrack
import numpy as np

energies = np.array([10.0, 50.0, 100.0, 500.0])  # MeV/u
betas = pyamtrack.converters.beta_from_energy(energies)
print(f"Betas: {betas}")

Python List Input

import pyamtrack

energies = [10.0, 50.0, 100.0, 500.0]  # MeV/u
betas = pyamtrack.converters.beta_from_energy(energies)
print(f"Betas: {betas}")

Edge Cases

• Zero Energy:

  beta = pyamtrack.converters.beta_from_energy(0.0)
  print(f"Beta for zero energy: {beta}")  # Output: 0.0

• Empty Input:

  betas = pyamtrack.converters.beta_from_energy([])
  print(f"Beta for empty input: {betas}")  # Output: []

Error Handling

• If the input is not a valid type (float, int, numpy.ndarray, or list), the function raises a ValueError or RuntimeError.
• Example:

  try:
      beta = pyamtrack.converters.beta_from_energy("invalid")
  except ValueError as e:
      print(f"Error: {e}")