[FLASH-USERS] Magnetic resistivity SpitzerHighZ

[Boyle, Gregory]

Hi Yingchao, 

It would appear that \tau_{ei} is an "energy-exchange" collision time, rather than the electron-ion collision time \tau_e. The relation between the two is: 

\tau_e = \tau_{ei}*2*m_e/m_i 

which explains the three-order discrepancy. That said, I agree that it should be the electron-ion collision time \tau_e rather than \tau_{ei} that is used in the magnetic resistivity calculation. (The \tau_{ei} should and does get used in the calculation of heat exchange.) 

Cheers, 
Greg. 


From: "Yingchao Lu" <yingchao.lu at gmail.com> 
To: "flash-users" <flash-users at flash.uchicago.edu> 
Sent: Wednesday, 21 November, 2018 01:32:06 
Subject: [FLASH-USERS] Magnetic resistivity SpitzerHighZ 

Hi FLASH users, 

It seems the magnetic resistivity for Spitzer HighZ in FLASH is three orders of magnitude smaller than those found in the literature. 

The code in source/physics/materialProperties/MagneticResistivity/MagneticResistivityMain/SpitzerHighZ/MagneticResistivity_fullState.F90 calculates the electron-ion equilibrium time 
res_ieEquilTime(zbar, abar, tele, tion, nion, eqtime) 

And the code in source/physics/materialProperties/MagneticResistivity/MagneticResistivityMain/SpitzerHighZ/res_ieEquilTime.F90 
eqtime = res_ieTimeCoef * & 
3.0 * res_boltz**1.5 / (8.0 * sqrt(2*PI) * res_qele**4) * & 
(mion * tele + res_mele * tion)**1.5 / & 
( sqrt(mion*res_mele) * zbar**2 * nion * ll) 

When Ti=Te, we can make some approximation, shown in the attached file. 

There are several references for Spitzer magnetic resistivity and they are consistent with each other. 
[ http://people.hao.ucar.edu/judge/homepage/PHSX515/fall2012/Braginskii1965.pdf | http://people.hao.ucar.edu/judge/homepage/PHSX515/fall2012/Braginskii1965.pdf ] 
[ https://www.cfa.harvard.edu/~namurphy/Lectures/Ay253_04_BeyondIdealMHD.pdf | https://www.cfa.harvard.edu/~namurphy/Lectures/Ay253_04_BeyondIdealMHD.pdf ] 
Physics Reports 417 (2005) 1–209 

I think the (7) to (10) in the image should be correct. Could any one double check? 

Thanks, 
Yingchao 

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