Problem 2169

Summary: Magnetic Monopole Ionization Model (Low Beta)
Product: Geant4 Reporter: Martin Frank <mfrank>
Component: processes/electromagneticAssignee: Vladimir.Ivantchenko
Status: RESOLVED FIXED    
Severity: normal CC: daren.sawkey
Priority: P4    
Version: 10.4   
Hardware: All   
OS: All   

Description Martin Frank 2019-06-25 23:03:49 CEST 
Hello,

We are simulating low velocity monopoles (beta < 1e-2) using Geant4 for our NOvA analysis and we noticed that the energy deposition model (G4mplIonisationWithDeltaModel.cc) is different from the theoretical model (Ahlen & Kinoshita).  The current Geant4 code (10.4.p2) that we use gives us twice the energy when compared to the theory.  Below follow some of the details.


Here is the code:
http://www-geant4.kek.jp/lxr/source/processes/electromagnetic/highenergy/src/G4mplIonisationWithDeltaModel.cc?v=10.4.p2#L141


When I look at the theory (S.P. Ahlen and K. Kinoshita, Phys. Rev. D26 (1982) 2347, reference [3] in code), I get the following equation for dE/dx (Eq. 33 combined with Eqs. 20, 35, and 36):

dE/dx = a * N^(1/3) * [log(b * N^(1/3)) - 0.5] * beta

where N is the electron density, beta the monopole velocity and a and b are given by:

a = pi * n^2 * hbar * c / (2 * (3*pi)^(1/3))

b = 2 * a0 * (3*pi^2)^(1/3)

where n is the quantized monopole charge (e.g. n = 1, 2, ...) and a0 is the Bohr radius.


The code implementation gives the same value for what I call b, but gives a value twice as large for a.  From the code (line 141), we have (ignoring the log term):

pi_hbarc2_over_mc2*eDensity*nmpl*nmpl/vF 
= pi * n^2 * hbar * c / ((3*pi)^(1/3))
= 2 * a


I am not an expert on the high velocity monopoles (beta > 1e-2), so I am not sure whether this factor of two is applicable there as well.

Would you please have a look at the code to see whether you come to the same conclusion?

Thank you for your help!
Regards,
Martin
Comment 1 Vladimir.Ivantchenko 2019-07-02 16:17:13 CEST 
Hello Martin,

thank you very much for investigation of this problem. I agree that there is factor 2 error in low-energy approximation. The fix will be available with the new Geant4 public version and also may be propagated backward. Cannot say to which versions. If you are using the code now likely optimal will be add factor 0.5 privately.

Another problem: the code should be modified for conductors, current version assume low conductivity of media like in Silicon. At this point I do not see an easy solution for today.

Vladimir
Comment 2 Martin Frank 2019-07-02 16:58:16 CEST 
Dear Vladimir,

Wow, thank you for your fast response!

Yes, we have gone ahead and patched the code with a local factor of 0.5 for now.  We will keep an eye out for what versions will be patched and then use them appropriately.

Fortunately, we are only interested in the energy deposition in liquid scintillator, so the low conductivity assumption works for us.

Thanks again,
Martin
Comment 3 Vladimir.Ivantchenko 2019-07-11 01:42:39 CEST 
The fix is already integrated into development version. The problem is fixed.