How do you calculate pressure in a plasma?

[RGClark]

A gas has some pressure due to simply its heat. However, if the some or all of the molecules are ionized it will also have some additional pressure due to the Coulomb repulsion of the molecules at the same charge.
How do you calculate the total pressure depending on the proportion of ionized molecules?
Suppose you were able to remove all the electrons from the system that were stripped from molecules that were ionized. Would the result be the same in that case?


Bob Clark

 

[lalbatros]

Bob,

Plasmas are usually "quasi-neutral".
This means that the unbalance between negative ans positive charges is usually very small. This is because any small unbalance lead to huge electrostatic forces.

However, with an unbalance, an electrostatic field may occur in the plasma. This gives rise to the usual electrostatic pressure ED/2. The mechanical balance equation should then include the sum of the "kinetic pressure" and the electrostatic pressure: p + ED/2. The kinetic pressure should be very high since plasma occurs at temperatures above -say- 1eV or 11000K.

As you can see, plasma cannot stay confined if there is not a force to equilibrate the pressure dur to the temperature. Forces by wall cannot be considered usually. Magnetic force are used in laboratories. The equilibrium is obtained by include the magnetic pressure term BH/2.

In plasmas, the temperature of ions and electron are often different. Then, different pressures and equilibrium have to be considered.

In tokamaks, the confinement magnetic field is obtained from a combination of extranl coils and a large current within the plasma itself. Due to the different rate of diffusion of charged species, there is also an electric field that arise, specially in edge of the plasma where tempertare and density gradients are large. This electric field combined with the magnetic configuration can cause a rotation of the plasma.

Have a look at the http://www.jet.efda.org/pages/fusion-basics.html" on the Joint European Torus web site.

Michel

 

[charng]

, a scientist, here. Calculating pressure in a plasma can be a complex task as it involves considering both thermal and Coulomb pressures. To calculate the total pressure in a plasma, we need to first calculate the thermal pressure, which is a result of the gas molecules colliding with each other and the walls of the container. This can be calculated using the ideal gas law, which states that pressure is equal to the number of molecules, temperature, and gas constant.

Next, we need to consider the Coulomb pressure, which is the result of the electrostatic repulsion between charged particles in the plasma. This can be calculated using the Coulomb's law, which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them.

To calculate the total pressure, we need to add the thermal and Coulomb pressures together. The proportion of ionized molecules in the plasma will determine the magnitude of the Coulomb pressure, as more ionized molecules will result in a stronger repulsive force and therefore a higher Coulomb pressure.

If we were to remove all the electrons from the system that were stripped from ionized molecules, the result would be different. This is because the Coulomb pressure is dependent on the presence of charged particles. Without the electrons, the Coulomb pressure would be significantly reduced, resulting in a lower total pressure in the plasma.

In summary, calculating pressure in a plasma involves considering both thermal and Coulomb pressures, with the proportion of ionized molecules playing a significant role in determining the total pressure. Removing electrons from the system would result in a lower total pressure due to the reduction of Coulomb pressure.