Search

• 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 %),

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.

Imagine evaporating a body of liquid with surface area $S$. Assume that during this process all the liquid molecules are separated and tLat each molecule can be considered a small particle with a definite surface area. Obviously, the total surface area of all these molecules is much greater than the surface area of the original body. Given that the latent heat of vaporization of water is $L=2.1\cdot 10^{6}J\cdot \;\mathrm{kg}^{-1}$ and that its surface tension is $α=7.2\cdot 10^{-2}N\cdot \;\mathrm{m}^{-1}$, estimate the size of water molecules.

Design an experiment to measure the dependence of the speed of evaporation on the surface area of the evaporating liquid. You should use at least five different containers to do the measurment. What other factors can influence the speed of evaporation? Note that this experiment should run for several days so plan accordingly.

• 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.

• 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 $r⁄R_{0}$.

• 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.

• 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.

• 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 $n$.

They have a new attraction in „Dolni Dvur“: Helium filled soap bubble, which are just levitating in the air. What is heavier? Helium in bubble or its wall?