[FLASH-USERS] Magnetic resistivity SpitzerHighZ

[Yingchao Lu]

Hi Greg,

Thanks for your explanation. I wrote down the correct formula with Z
dependency from those in Braginskii. I modified the code as attached. The
Coulomb log remains the same.

Could anyone else check if the attached formula is correct?

Thanks,
Yingchao

On Fri, Nov 23, 2018 at 6:33 AM Boyle, Gregory <gregory.boyle at desy.de>
wrote:

> 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
> 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
> [image: Screen Shot 2018-11-20 at 5.26.52 PM.png]
>
>
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