Taylor Element coordinates

[danielkallendorf]

A Taylor element represents a transformation of particle coordinates by applying a truncated power series to the coordinates.
This requires precise definition of the coordinates and pals must be able to convert representations.

I will try to collect possibilities here:

• x- and y-position are not ambiguous up to the unit, but we will require PALS-standard units here.
• Angles can be given by
  • momenta $p_x$ or normalized momenta $p_x/p_0$, where $p_0$ is the reference momentum
  • slopes: $x'=dx/ds$ or equivalently $p_x/p_z$
• The longitudinal coordinates can be given
  • by $l=\delta z$,
  • a normalized version of $l$
  • a Time-of-Flight offset $\Delta t$
• The longitudinal change
  • $\delta=\Delta B\rho$
  • relative kinetic energy $\delta_K$

Additionally parameters like charge or mass can be included.
Are there other conventions?

The conversion process between the bases is not entirely trivial and requires information about the beam.
But having this as part of PALS would be extremely convenient for my field of research.

[DavidSagan]

With "lattice expansion" that the PALS translator will be able to do, the reference energy and reference particle will be known so that the translator will also be able to do coordinate translations. One thing that is needed is to decide what set of coordinates to support. Someone want to start on a list? Note: In terms of units, I would have the standard stick to the the units that are already defined in the standard (positions in meters, etc.). Any program can convert between the units the program is using and PALS units.

[cemitch99]

For the longitudinal phase space, two additional normalizations of the variables you list are:

• coordinate: $c\Delta t$, momentum: $-\Delta E/p_0c$
• coordinate: $-c\Delta t$, momentum: $\Delta E/p_0c$

where $p_0$ is the design momentum, and $\Delta E$ is the deviation of energy from the reference value. These are both used. (The first is used in ImpactX.)