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## Re: Space varying Magnetic Field Problem

Forum: Fields: Magnetic and Otherwise
Re: Space varying Magnetic Field Problem (Michael Rinaldi)
Date: 07 Jun, 2010
From: John Apostolakis <John Apostolakis>

 ```Dear Mike, The key question is not whether the track you obtain is smooth - it is whether it is accurate enough. And it is not simple to answer whether or not you are providing an accurate enough description of your magnetic field with your relatively coarse 3D grid. It depends on the accuracy requirements for the tracks which are most sensitive for your application. It is not clear from your description what type of field you are modeling - and this affects significantly the answer. If the field has large gradients or changes direction in the region you are traversing (with particles), then the linear interpolation is likely a poor description. This will affect the quality of the results. I can see two ways to estimate if your track is accurate enough for your requirements: - to compare a simulation with the current coarse grid (1 cm^3) to one with a finer grid e.g. (0.1cm)^3 checking the endpoint of a key particle or key observable that you will measure ( e.g. propagating a muon through it and seeing where it ends up, or measuring the energy deposition in a few smallish volume that is important). Unless your field is very non-uniform - to do a numerical integration the difference between a fully accurate and a coarse description of the field for a few typical tracks. Likely this is easier outside Geant4 than inside it. The default stepper (G4ClassicalRK4) is not ideal for fields which are not smooth up to 2nd or 3rd derivative - but it is robust, so it will give you a reasonable answer. In the absence of the higher derivatives, it will not make as efficient use of the field evaluations as a lower order stepper. For fields which do not have continuous higher derivatives, we recommend G4SimpleRunge or G4SimpleHeum. If you make a comparison of their efficiency and accuracy, we will be interested in your results. Finally I note that linear interpolations are simple and fast, but more sophisticated interpolation methods which take into account that they are approximating a magnetic field, while costlier to compute, are much better suited to high order Runge-Kutta solvers. Regards, John On Jun 8, 2010, at 1:24 AM, Michael Rinaldi wrote: > > *** Discussion title: Fields: Magnetic and Otherwise > > Hi folks, I've constructed a model that implements a 3D space > varying magnetic field in a particular volume. The field is read in > from a file and is a set of values of Bx, By, and Bz. The field > values are defined on a 1 cm grid. I wrote the GetFieldValue() > function to return the pertinent field components as needed by the > stepper. My problem is that > I get vastly different steps by changing the field value slightly. > > The function GetFieldValue(const G4double point[4], double *field) > that is required from me is written so that each time it is called > my code does a tri-linear interpolation on my 3D grid to find the > field at the input point from the stepper > point[0],point[1],point[2]. I'm thinking that since this > interpolation is happening on a coarse 1cm x 1cm x 1cm > grid then the field values are not smooth enough to give a good > smooth track. > > I'd like some advice as to the best way to proceed. Should I > increase the grid by a factor of 10 so that it is defined every 1mm > instead of 1cm or should I use a different stepper. Currently I'm > simply using > > G4ChordFinder *chordFinder = new G4ChordFinder(magField, stepMinimum); > > which I believe uses the RK4 stepper. If I need to change the > stepper how do I do that? > > Thanks, Mike > > ------------------------------------------------------------- > Visit this GEANT4 at hypernews.slac.stanford.edu message (to reply > or unsubscribe) at: > http://hypernews.slac.stanford.edu/HyperNews/geant4/get/emfields/171.html ```

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