Formula momentum conversion

• Add two functions to Utilities/Util
• Update documentation

Summary

I'm not sure if this is a bug, but I don't understand the formula used to convert P [eV/c] to

$\beta\gamma$

[dimensionless] in the function Distribution::converteVToBetaGamma:

$$(\beta_x\gamma)=\sqrt{(\frac{P_x[{eV/c}]}{m_0c}+1)^2-1}.$$

If the user gives momentum in eV/c, I would imagine that the conversion should be

$$\gamma\beta_x = \frac{P_xc}{mc^2}.$$

If it's not a bug then I think it should be better explained in the manual.

added Bug label

changed milestone to %OPAL 2.4.0

@adelmann @snuverink_j @kraus any comments on this?

I had a discussion with @albajacas_a about this at some point. Then we didn't really manage to understand it, but the formula comes from

$$\gamma = \frac{E}{\text{massIneV}} + 1.0 \\$$

$$\beta = \sqrt{1.0 - \frac{1.0} {\gamma^{2}}}$$

From this it follows:

$$\beta * \gamma = \sqrt {\gamma^{2} - 1.0} = \sqrt{(\frac{E}{\text{massIneV}}+1)^2-1}$$

It seems that this method is mostly used with momenta. Only the emission models use it with a kinetic energy.

The name of the method should also make it clear whether it converts momenta or energy.

Ah OK now I understand the formula, but then it is transforming kinetic energy to momentum. I think that this makes sense for the emission models, where p_mean is along the z-axis only

    double wThermal = std::abs(Attributes::getReal(itsAttr[Attrib::Distribution::EKIN]));
    pTotThermal_m = converteVToBetaGamma(wThermal, beam->getM());
    pmean_m = Vector_t(0.0, 0.0, 0.5 * pTotThermal_m);

but IMO it doesn't make sense to use it for the momenta in three directions like here

    if (inputMoUnits_m == InputMomentumUnitsT::EV) {
        sigmaP_m[0] = converteVToBetaGamma(sigmaP_m[0], massIneV);
        sigmaP_m[1] = converteVToBetaGamma(sigmaP_m[1], massIneV);
        sigmaP_m[2] = converteVToBetaGamma(sigmaP_m[2], massIneV);
    }

I think the current converteVToBetaGamma should be renamed to convertEkinToMomentum, and then there should be another function like convertMomentumeVToBetaGamma which returns

$$\gamma\beta_x = \frac{P_xc}{massIneV}.$$

Do you agree? Then we can also correct it in the manual

@snuverink_j @kraus If you agree with this I will make a merge request and fix it

Yes please. But don't we already have a method to convert from the kinetic energy to the momentum (e.g. in Utilities/Util.h)? I would place the method to convert from eV to beta gamma also in Util.h.

@albajacas_a Agreed, and yes please. And as Christof mentioned, put the methods in a more common place. Classic/Utilities/Util seems good.

In Utilities/Util.h there are already three similar functions: getGamma, getEnergy, getP. I suggest that in the wake of these changes you also name the latter two of these functions more appropriately, e.g. getKineticEnergy and getBetaGamma.

changed the description

assigned to @albajacas_a

created merge request !385 (merged) to address this issue

mentioned in merge request !385 (merged)

changed the description

@snuverink_j @kraus

could one of you give me access to the manual repository so that I can update this in the documentation, please? (https://gitlab.psi.ch/OPAL/documentation/manual)

We don't have enough rights. @frey_m @gsell : can you do this?

@albajacas_a @snuverink_j Done.

marked the checklist item Add two functions to Utilities/Util as completed

mentioned in issue OPAL/documentation/manual#36 (closed)

marked the checklist item Update documentation as completed

changed due date to July 24, 2020

closed

marked this issue as related to OPAL/documentation/manual#36 (closed)

mentioned in commit regression-tests@7777cf7d

added Add/modify Doc label

mentioned in issue #649 (closed)