[FLASH-USERS] Magnetic resistivity SpitzerHighZ

[Yingchao Lu]

Corrected a typo in the last screenshot.
[image: Screen Shot 2018-11-29 at 10.37.41 AM.png]

On Thu, Nov 29, 2018 at 10:35 AM Yingchao Lu <yingchao.lu at gmail.com> wrote:

> 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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