Add Pedestal Europed Parameteristion #1406

Open jonmaddock opened 2 years ago

In GitLab by @ajpearcey on Sep 27, 2021, 09:14

Samuli has shared with us a pedestal parameterisation that we can implement in PROCESS and test it out. See below for the datails.

From: Saarelma, Samuli samuli.saarelma@ukaea.uk, Sent: 12 November 2021 16:33
Subject: Corrected parameterisation

It turned out that the pedestal parameterisation that I sent was done too hastily by just multiplying density (in 10^19 m^-3) and temperature (in keV) and was missing the electron charge when representing the pressure in kPa. So, the corrected parameterisation for the electron pedestal pressure should be:

Pe_ped [kPa] = 0.46 delta^1.69 Bt[T]^0.41 Ip[MA]^1.44 * neped[10^19] ^ 0.40.

One more thing that I didn’t mention was that this was done assuming Ti=Te, Zeff=1.8 and Zimpurity = 54. If you adjust the impurities (and thus change the dilution), then as a rule of thumb, the electron pressure should be adjusted so that the total pressure stays fixed. In STEP with that high Zimpurity it doesn’t make much of a difference, though.

Michael asked for the parameter ranges used to derive the scaling. They are the following:

delta = 0.5-0.57 (this range looks small, but I’ve done a much bigger scan for a wider range of triangularity for some individual cases and seems to apply there as well)
Bt = 2-3 T
Ip = 17-25 MA
neped = 5-14 x 10^19 m^-3

From: Saarelma, Samuli samuli.saarelma@ukaea.uk, Sent: 15 November 2021 08:47

So, the scaling is done based on the pedestal being marginally stable (or in other words, “just before an ELM”). To take into account ELM mitigation, it should be scaled down by the 0.8 factor. In fact, it’s better to do that correction to it even if you assume ELMy plasmas, as then it will predict the “ELM averaged” pedestal instead of “just before an ELM”.

From: Saarelma, Samuli samuli.saarelma@ukaea.uk, Sent: 12 November 2021 12:18

If you run PROCESS with fixed H-factor, then using the pedestal model makes little sense, especially if it leads to higher fusion power at lower pedestal. With fixed H-factor, I’d rather suggest just running with fixed T0/T_ped ratio (like 5?) so that at least your profile shapes are reasonable. The pedestal model in PROCESS makes sense only if you don’t prescribe the confinement is determined by the core transport model + pedestal.

The parameters that I have found have very little effect on the pedestal prediction are beta and separatrix density. Ellipticity 
seems to have a negative effect at high beta but almost no effect at low beta. So, that’s why I haven’t included it in the scaling. 

I’ve also concluded a size scan, so keeping the aspect ratio fixed and scaling R. That gives an extra scaling factor:

(R/R_SPR008) ^ -2.1 .

If the aspect ratio is changed, you can use the scaling: 
(R/R_SPR008) ^ -1.34 * (a/a_SPR008) ^ -0.74. 

This scaling is probably not perfect, but it should be much better suited for STEP than any scaling for ITER or DEMO. 

If you have any questions, please let me know.

Cheers,

Samuli

P_{ped}=0.8\times 460\text{ Pascal} \times \delta^{1.69} 
(\frac{Bt}{T})^{0.41} 
(\frac{Ip}{MA})^{1.44} 
(\frac{n_{ped}}{10^{19}m^{-3}})^{0.40}
(\frac{R}{3.639 \text{m}})^{-1.34}
(\frac{a}{2.183 \text{m}})^{-0.74}

where
$P_{ped} = \text{electron pressure at the pedestal} ={n_{ped}} {T_{ped}}$
n = electron density
T = electron temperature
R = major radius
a = minor radius

In GitLab by @mkovari on Oct 5, 2021, 13:50

Please remember to read Issue #413, especially the following:

If you run it with fixed H-factor, the teped effect is likely to be minimal, because your code is going to penalise the core confinement when the pedestal temperature increases. When you have the core transport model, and especially if it’s a critical gradient model (grad T/T \~ constant through the profile), you should see much higher H-factors when you increase the pedestal temperature. And this better confinement should then translate to more fusion power and smaller device.

As @rkemp pointed out in March 2016 (!), the effect is perverse: reducing the pedestal with fixed H-factor increases the central temperature, and therefore reduces the major radius. For the time being we need to keep the pedestal scaling switched off.

In GitLab by @mn3981 on Oct 18, 2021, 14:00

created branch 1405-add-pedestal-europed-parameteristion to address this issue

In GitLab by @mn3981 on Oct 22, 2021, 11:41

The equation for pedestal pressure has an error in the form of an extra asterisk between delta and Bt, and needs corrected to:

P_ped [kPa] = 0.29 * delta^1.69 * Bt[T]^0.41 * Ip[MA]^1.44 * neped[10^19] ^ 0.40. (delta = triangularity)

This may have caused confusion with delta being raised to the power of Bt, but is just a simple multiplication.

In GitLab by @mn3981 on Oct 28, 2021, 15:14

created merge request !553 to address this issue

In GitLab by @mkovari on Nov 1, 2021, 10:32

Well spotted.

In GitLab by @mkovari on Nov 12, 2021, 10:07

I note that Issue #730 (add scaling factor to eped model) has an additional factor eped_sf:

    !! Adjustment factor for EPED scaling to reduce pedestal temperature or pressure 
    !! to mitigate or prevent ELMs

This has been included in the new scaling function but the default value is 1. Samuli:

the factor is to accommodate the idea that we can’t operate at the peeling-ballooning boundary as there we would get ELMs. The scaling was derived based on the model that assumes that we’re on the boundary. So, a factor of 20% (so I guess 0.8 in eped_sf) should be used to mimic the ELM suppression effect on the pedestal. We don’t exactly how the ELM suppression would be done, but we can estimate that it would lower the pedestals so that they stay below the stability limit.

In GitLab by @mkovari on Nov 12, 2021, 11:09

The message from my comment above about H-factor is that it would be nice to run using a number of values of eped_sf. (You could even make it bigger than 1 for fun.) You may find that this gives perverse results.

In GitLab by @mkovari on Nov 12, 2021, 14:14

Also we need to have the range of applicability.

In GitLab by @mkovari on Nov 12, 2021, 16:19

If we use assume stiff profiles in a logarithmic sense (GradT/T) then we could fix T0/Tped. If we assume that H=1 for a specified set of parameters giving a particular pedestal temperature, then for a different set of parameters, we could recalculate T0, giving a new value of the thermal energy content of the plasma, giving a new value of H.

This is frankly dubious. We would need to speak to a core confinement specialist.

ukaea / PROCESS

Add Pedestal Europed Parameteristion #1406