# Serial of year 26

You can find the serial also in the yearbook.

*We are sorry, this serial has not been translated.*

## Text of serial

## Tasks

### (6 points)1. Series 26. Year - S. series

- Find out typical properties of a plasma present is the solar wind, in the center of a tokamak and in a low-pressure discharge and calculate the corresponding value of $λ_{D}$.

- Derive an expression for the Debye length of plasma that consists of electrons at temperature $T_{e}$ and ions at temperature $T_{i}$. Do not assume that the ions are static.

- Calculate the electrostatic potential of two infinite parallel conducting planes that are separated by a distance $d$. The potential on these planes is kept $φ=0$ and the space in between these planes is filled with a gas of particles with charge $q$ and concentration $n$.

Robin

### (6 points)2. Series 26. Year - S. drifting

- What kind of drifts can we observe in a linear trap? Assume that the axis of the trap is horizontal. Will the drift caused by the gravitational force have a significant effect on the motion of a particle?

- Derive a formula for the loss cone and draw an original picture illustrating the behavior of a particle in a linear trap.

- Derive a formula for the drift caused by an electric field that is perpendicular to a magnetic field and that has a constant gradient parallel with the electric field. Discuss the the dependence of the particle trajectories on the magnitude of this gradient.

### (6 points)3. Series 26. Year - S. tokamak

- Calculate the specific resistance of hydrogen plasma at temperature 1 keV. Compare your result with the resistance of common conductors.

- Calculate the current necessary to create a sufficiently strong poloidal magnetic field in a tokamak with a major radius of 0.5 m. The toroidal field is created using a toroidal coil with 20 windings per meter. The current inside this coil is 40 kA. The magnitude of the poloidal field should be approximately 1/10 of the magnitude of the toroidal field.

- Create a physical model of the field lines of the force field inside the tokamak, take a photo of it, and send it to us.

### (6 points)4. Series 26. Year - S. More tokamaks

- Using the expression for the frequency of impacts from the last part of this series, derive a formula for the diffusion coefficient of classical diffusion and calculate its value for a typical plasma in a tokamak.

- Derive a formula for the dependence of the fraction of captured particles on the ratio of the main and small plasma radius $r⁄R_{0}$.

komm

### (6 points)5. Series 26. Year - S. series

- Go to this site http://fykos.cz/rocnik26/4-compass.dat and download data gathered with a Langmuir probe from the tokamak COMPASS. Draw the volt-ampere characteristic and estimate the value of the floating potential.

- Given the surface area of the probe ($A=6\;\mathrm{mm}^{2})$ and the composition of the plasma (deuterium), analyze the volt-ampere characteristic and determine the value of electron temperature and density.

- Write a short ode describing the invention of the Langmuir probe.

Robin.

### (6 points)6. Series 26. Year - S. series

- Calculate the time a tokamak COMPASS can store an energy for. The energy of its plasma is 5 kJ, and its ohmic heating is 300 kW.

- Calculate the alpha heating in tokamak COMPASS if it used a DT mixture. Typical plasma temperature is 1 keV, hustota 10^{20} m^{ − 3}, and the volume of the plasma 1 m. Assuming the ohmic heating from the preceeding question, calculate $Q$.

- Using the picture from the main text and knowledge of the DD reaction ^{2}_{1}D + ^{2}_{1}D → ^{3}_{2}He + n + 3,27 MeV (50 %),

{2}_{1}D + | {2}_{1}D → |
---|

¾ energie v of the energy in the first reaction are carried off by a neutron, calculate the total plasma heating that will occure during one DD reaction (assume that it is followed by a DT fusion with the product of the second reaction). Also estimate the requirements on the confinment time assuming density odhadněte nároky na dobu udržení při hustotě 10^{20} m^{ − 3} a teplotě 10 keV.

Robin