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# RRFMuon v1¶

## Summary¶

Calculate Muon asymmetry in the rotating reference frame (RRF).

## Overview¶

This algorithm provides a method for making a rotating reference frame transformation, which provides a useful method of visualising high frequency signals. Since the transformation leaves a comparatively low frequency signal, the data can readily be rebinned to improve counting statistics - this is particularly useful during an experiment to provide an early check on the form of the measured signal. Data analysis (for example least squares fitting) to study the form of the signal relaxation can be completed in either the laboratory or rotating reference frame according to preference.

This algorithm is frequently run after making a phase quadrature transformation using the algorithm PhaseQuad v1. Both algorithms are fully described in the article by T.M. Riseman and J.H. Brewer [Hyp. Int., 65, (1990), 1107].

CalculateMuonAsymmetry

## Properties¶

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

Name of the input workspace containing the spectra in the lab frame

OutputWorkspace

Output

MatrixWorkspace

Mandatory

Name of the output workspace containing the spectra in the RRF

Frequency

Input

number

0

Frequency of the oscillations

FrequencyUnits

Input

string

MHz

The frequency units. Allowed values: [‘MHz’, ‘Gauss’, ‘Mrad/s’]

Phase

Input

number

0

Phase accounting for any misalignment of the counters

## Description¶

Assuming InputWorkspace contains the real and imaginary parts of the asymmetry in the lab-fram, the algorithm returns the muon polarization in the Rotating Reference Frame (RRF), given the frequency of the oscillations and the phase of the detectors, as given by the formula:

$P_R^{RRF} (\nu_0, \phi, t)= + P_R\left(0,t\right) \cos\left(2\pi\nu_0 t + \phi\right) + P_I\left(0,t\right) \sin\left(2\pi\nu_0 t + \phi\right)$
$P_I^{RRF} (\nu_0, \phi, t)= - P_R\left(0,t\right) \sin\left(2\pi\nu_0 t + \phi\right) + P_I\left(0,t\right) \cos\left(2\pi\nu_0 t + \phi\right)$

where $$P_R\left(0,t\right)$$ and $$P_I\left(0,t\right)$$ are the real and imaginary part of the asymmetry in the lab-frame, $$\nu_0$$ is the input frequency, and $$\phi$$ the input phase.

## Usage¶

Example - Computing asymmetry in RRF

import math
# Create an input workspace with two spectra
datax = [i/100. for i in range(1,300)]
datay1 = [ math.cos(2*3.14159*i/100.) for i in range(1,299) ]
datay2 = [ math.sin(2*3.14159*i/100.) for i in range(1,299) ]
datay = datay1 + datay2
input = CreateWorkspace(dataX=datax, dataY=datay,Nspec=2,UnitX="TOF")
# Compute polarization in RRF
output = RRFMuon(input,1.0,"MHz",0)


Output:

1.0
-0.0


Categories: AlgorithmIndex | Muon