Choose timezone
Your profile timezone:
Powered by Indico
v3.3.5
Meeting Location: 7.2-001
Zoom Raum 2 (ID: 948-1054-7070 / PW: 021741)
Dear colleagues,
Thank you for your continued interest in divertor design!
The next colloquium is scheduled for Tuesday 26.03. from 16:30 to 17:30 in Room 7.2-001 and Zoom Raum 2 (ID: 948-1054-7070 / PW: 021741)
https://event.ipp-hgw.mpg.de/event/1325/
On the Agenda is the multi reservoir model of Core, Edge, Plasma SOL, Divertor SOL, and PFR for tokamaks and stellarators and the resulting exhaust and screening efficiencies.
Slides and Minutes from the previous colloquia can be found under:
https://event.ipp-hgw.mpg.de/category/63/
Below are the Minutes from this week:
We unfolded the toroidal cross section along a field line from plasma stagnation point to divertor stagnation point. For this we assumed a homogenous D_perp for the plasma and for the divertor toroid, which puts it at half the connection length of the last closed plasma flux surface (LCPFS) and last closed divertor flux surface (LCDFS). The pressure at this stagnation point is highest and drives plasma transport away from it. In reality D_perp is not homogenous but depends on confinement and therefore the magnetic field. In the case of a Tokamak with the bad curvature on the outboard side, this puts the stagnation point somewhere on the outer midplane, depending on the plasma shaping.
Along this field line we discussed the different regimes of perpendicular and parallel transport. We have three known transport mechanisms: Diffusive, Neo-classical, and Turbulent. All mechanisms transport plasma from regions of high concentration to low concentration and can therefore be combined as one D_perp. While the exact value is typically a-posteriori knowledge, the existence of a D_perp can be seen as a-priori.
We discussed if the particle distribution in P-SOL, D-SOL, and PFR was exponential or Maxwellian.
The Maxwell-Boltzmann distribution is primarily used to describe the distribution of particle speeds in a gas at a certain temperature. However, besides particle speeds, it can also be applied to describe other properties of particles in a gas, such as their kinetic energy, momentum, and the distribution of velocities in different directions.
Here are some additional applications of the Maxwell-Boltzmann distribution:
Kinetic Energy Distribution: The distribution can be used to characterize the distribution of kinetic energies of particles in a gas. This is important in understanding phenomena such as energy transfer, collisions, and heat capacity.
Momentum Distribution: By considering the velocities of particles in different directions, the Maxwell-Boltzmann distribution can provide insights into the distribution of momenta in a gas. This is relevant in studies involving momentum transfer, pressure, and diffusion.
Thermal Conductivity: The distribution of particle speeds affects the rate of thermal energy transfer through a material. Understanding the distribution of velocities helps in modeling thermal conductivity, which is crucial in various engineering applications.
Diffusion: In the context of diffusion, the distribution of particle velocities influences the rate at which particles move from regions of high concentration to low concentration. The Maxwell-Boltzmann distribution provides insights into the statistical behavior of particles undergoing diffusion.
Chemical Reactions: In chemical kinetics, the Maxwell-Boltzmann distribution is used to describe the distribution of kinetic energies of reactant molecules. This distribution influences the rate at which chemical reactions occur, as it determines the fraction of molecules with sufficient energy to overcome the activation energy barrier.
Overall, the Maxwell-Boltzmann distribution is a fundamental concept in statistical mechanics and plays a crucial role in understanding various physical and chemical processes involving gases and particles.
A. Loarte used an exponential distribution for the P-SOL but a Maxwellian for the D-SOL. The difference is the derivative at the separatrix. If we have a flat profile, i.e. L-Mode Tokamak, it makes sense to use a Maxwellian. For a steep profile, i.e. H-Mode Tokamak, an exponential function is better suited.
For the definition of the density width 6 sigma lamda_n this does not make a difference, as the statistical approach works for both assumptions. The 6sigma lamda_n width is defined by the width that inhibits 6 sigma of particles. Using the same method widths of 1, 2, 3, 4, 5 sigma can also be defined.
Particles cross the separatrix from the edge into the P-SOL. Integrating along the connection length this will build up a density profile which has its minimum at the stagnation point and its maximum at the X-Loop. At the X-Loop a transition from the P-SOL to the D-SOL happens. At this point the D_perp changes from D_perp,plasma to D_perp,divertor. The source from the edge is no longer present, instead there is a density step function into the PFR. The built up density profile from the P-SOL relaxes into the D-SOL and PFR. The strong density gradient to the PFR will shift the density peak slightly into the D-SOL. This maxwellian relaxation will lead to a spreading of the strike line, reaching its maximum width at the divertor stagnation point.
When considering parlallel transport, there can be a binormal perpendicular diffusion coefficient in stellarators which depends on the island rotational transform. This binormal perpendicular diffusion is a shortcut in the parallel direction as a particle can jump from on point on the field line, binormal to the same fieldline but further down in along it. This does not increase the strike line widening.
If we look at an island without any targets, and define the connection length as the length that a fieldline takes to close on itself, this length will shrink the higher the rotational transform of the island is. The island rotational transform determines the ratio of parallel to perpendicular transport along a fieldline. The fieldline length then determines how much time there is for this transport to happen.
So for an island with the same rotational transform, we’d get a wider SOL width the longer our connection length is.
For an island with the same connection length, we’d get a wider SOL with a lower rotational transform.
In an infinitely long field line in the divertor with a finite neutral pressure, the incoming plasma would ionize the neutral gas, decreasing the plasma temperature and increasing its density. The density profile along the fieldline can also be described by a maxwellian distribution. In the 2-point model the “upstream” location is set at the X-loop, with the downstreamlocation at the target. The ratio of upstream to downstream density is often called the “recycling regime”, with n_u = n_d³ considered as the high recycling regime. This depends on how many neutrals the plasma could already ionize and therefore drive up the downstream density. If we go past this, we eventually get a roll-over in the density, where the plasma transitions from an ionizing plasma to a recombining one.
Additionally to perpendicular transport, magnetic flux expansion can further spread out the particles in space. A flux expansion happens naturally going towards an X-loop, with a flux compression going away from an X-loop. A visualization of perpendicular transport and flux expansion/compression in one image is confusing, in particular when perpendicular transport leads to a widening of the density profile, while a flux compression counteracts this. For future visualizations and discussions it is better to separate both processes.
Thank you for your continued interest, input and the lively discussion!
Best,
Thierry