Thousands of drugs are currently in use, but only for a few of them experimental chronic fish data exist. Therefore, Huggett et al. (Human Ecol Risk Assess 2003; 9:1789-1799) proposed the fish plasma model (FPM) to extrapolate the potential of unintended long-term effects in fish. The FPM compares human therapeutic plasma concentrations (HPC(T)) with estimated fish steady-state concentrations (FPC(ss)), under the assumption that biological drug targets may be conserved across the species. In this study, the influence of using different input parameters on the model result was characterised for 42 drugs. The existence of structurally and functionally conserved protein targets in zebrafish could not be refuted. Thus, the FPM model application was not in contradiction to its basic assumption. Further, dissociation of drugs was shown to be important in determining the output and model robustness. As the proposed model for FPC(ss) estimation was considered to predict accurate values for neutral and lipophilic chemicals only, a modified bioconcentration model was used with D(OW) as predictor. Using reasonable worst case assumptions, a hazard was indicated for one third of the selected drugs. Our results support the notion that this approach might help to prioritise among in use drugs to identify compounds where follow up evidence should be considered.

Plasma modeling refers to solving equations of motion that describe the state of a plasma. It is generally coupled with Maxwell's equations for electromagnetic fields or Poisson's equation for electrostatic fields. There are several main types of plasma models: single particle, kinetic, fluid, hybrid kinetic/fluid, gyrokinetic and as system of many particles.


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The single particle model describes the plasma as individual electrons and ions moving in imposed (rather than self-consistent) electric and magnetic fields. The motion of each particle is thus described by the Lorentz Force Law.In many cases of practical interest, this motion can be treated as the superposition of a relatively fast circular motion around a point called the guiding center and a relatively slow drift of this point.

To reduce the complexities in the kinetic description, the fluid model describes the plasma based on macroscopic quantities (velocity moments of the distribution such as density, mean velocity, and mean energy). The equations for macroscopic quantities, called fluid equations, are obtained by taking velocity moments of the Boltzmann equation or the Vlasov equation. The fluid equations are not closed without the determination of transport coefficients such as mobility, diffusion coefficient, averaged collision frequencies, and so on. To determine the transport coefficients, the velocity distribution function must be assumed/chosen. But this assumption can lead to a failure of capturing some physics.

Although the kinetic model describes the physics accurately, it is more complex (and in the case of numerical simulations, more computationally intensive) than the fluid model. The hybrid model is a combination of fluid and kinetic models, treating some components of the system as a fluid, and others kinetically. The hybrid model is sometimes applied in space physics, when the simulation domain exceeds thousands of ion gyroradius scales, making it impractical to solve kinetic equations for electrons. In this approach, magnetohydrodynamic fluid equations describe electrons, while the kinetic Vlasov equation describes ions.[1] [2]

In the gyrokinetic model, which is appropriate to systems with a strong background magnetic field, the kinetic equations are averaged over the fast circular motion of the gyroradius. This model has been used extensively for simulation of tokamak plasma instabilities (for example, the GYRO and Gyrokinetic ElectroMagnetic codes), and more recently in astrophysical applications.

Quantum methods are not yet very common in plasma modeling. They can be used to solve unique modeling problems; like situations where other methods do not apply.[3] They involve the application of quantum field theory to plasma. In these cases, the electric and magnetic fields made by particles are modeled like a field; A web of forces. Particles that move, or are removed from the population push and pull on this web of forces, this field. The mathematical treatment for this involves Lagrangian mathematics.

Plasma modeling includes the description of phenomena such as the kinetics of charged and neutral species, mass transport, electromagnetic fields, heat transfer, and fluid mechanics. In this 6-part self-paced course, you will get an introduction to modeling plasma, with a focus on modeling nonequilibrium plasma, using the COMSOL Multiphysics software and the Plasma Module. This includes learning about the fundamentals of modeling plasma, best modeling practices, the underlying equations used for the plasma physics interfaces and physics feature nodes, and the various specialized capabilities and features in the Plasma Module. We also discuss the possibilities and limitations of plasma modeling using the software. In addition, you will see various demonstrations of how to create simulations of different types of plasma applications.

This course is meant for users that are familiar with COMSOL Multiphysics. If you are new to using the software we strongly recommend completing the introductory tutorial series for new users or attending a live, introductory training course before starting this Learning Center course. Additionally, some familiarity with the basic concepts of plasma physics is advantageous.


After completing this course, you will be knowledgeable in the relevant theory for plasma modeling and have a complete understanding of what the Plasma interface, as well as other interfaces, in COMSOL Multiphysics can be used for. You will also be aware of the various specialized features for plasma modeling, study types for analyses of plasma systems, and the additional resources available for learning more beyond the scope of this course.

In low-temperature plasmas with low ionization degrees, the dominant species are neutrals. This means that the electrons and ions are transported in a background of neutral gas (with which they primarily collide). For the plasmas we are interested in modeling, the electrons have much higher energies than all other species in the plasma, with the electron mean energy being of the order of a few electronvolts and the temperature of the background gas ranging from room temperature to about 1000 K.

In summary, the main elements of a plasma chemistry are its species and properties, including transport coefficients, electron impact reactions, heavy species reactions, and surface reactions. These are discussed in more detail below.


Figure 1. The Model Builder showing the Electron Impact Reaction features for a user-made plasma chemistry for a mixture of argon and oxygen. The Settings window is for the Electron Impact Reaction feature that ionizes the molecular oxygen. The reaction is specified by an electron impact cross section.

The source terms in the transport equations are computed using rate coefficients that represent the effect of collisions. For electrons, the best strategy for obtaining rate coefficients is to provide electron impact cross sections and make a suitable integration over the electron energy distribution function (EEDF). The reason for this is that the EEDF is not known a priori, and in low-temperature plasmas, the EEDF often deviates from a Maxwellian EEDF. By providing electron impact cross sections, the flexibility in changing the EEDF is preserved.


Figure 3. The Model Builder showing the Surface Reaction features for a user-made plasma chemistry for a mixture of argon and oxygen. The Settings window is for a Surface Reaction feature that specifies the neutralization of the argon ion at a surface as well as the emission of secondary electrons.

In a plasma reactor, a steady-state operation is achieved by balancing creation mechanisms with volume and surface losses. Frequently, surface losses are the dominant mechanism. In practice, this means that electron impact reactions create an electron-ion pair; the electrons are absorbed at a surface, whereas the ions are neutralized to the ground state. If no loss mechanisms are introduced for a given species (excited states included), the species can grow unbounded. Because of this, a steady state is not possible to achieve, leading to failure of the numerical simulation. Figure 3 shows how the Surface Reaction feature is used to apply a boundary condition for the ion Ar+ and to specify that the ion is neutralized to the ground state Ar at the surface. This is accomplished by typing Ar+=>Ar in the Formula field. Similarly, the reaction below Ars=>Ar states that the excited state or argon Ars is de-excited to the ground state.

When an ion or a neutral excited species reaches a surface, an electron can be emitted. This electron creation mechanism is crucial for the operation of direct current (DC) discharges and to achieve the high-power regime (also known as the gamma regime) in capacitively coupled plasma (CCP) reactors. This mechanism can easily be introduced in COMSOL by specifying a number different than zero in the Secondary emission coefficient field. In Figure 3, this option is set to 0.07, which means that the ion flux at the surface is multiplied by 0.07, and is given as a flux source to the electrons.

The fluid-type models used in COMSOL need transport coefficients for all species in the model. The main transport mechanisms are diffusion and migration in the electric field. These transport mechanisms are characterized by mobility and diffusion coefficients. A good estimation of the transport losses needs accurate transport coefficients. For electrons, the mobility plays an important role in how electrons absorb energy from the electric field.

Plasma chemistry and relevant data can be difficult to obtain, if not inexistent. A great deal of literature research is needed, as is a lot of guess work in many cases. Here, we highlight references that can be used to find data relevant for plasma chemistries. Reference 6, for example, presents how to develop plasma chemistries. The author also gives additional references for plasma chemistry data and discusses how to estimate data. References 2 and 3 are textbooks about plasma physics and plasma chemistry, and provide plasma chemistry data. Reference 5 contains examples of ion mobilities being used as a function of an electric field. To obtain electron impact reactions, we recommend the LXCat database. 006ab0faaa

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