Rules of thumb

Jarboe's 'Rules of Thumb' - basic associations and concepts to keep in mind when working with fusion plasmas

Rule 1

In event counting measurements the uncertainty in event rate is equal to the square root of the number of events detected. A trade off is made between signal resolution and time resolution

Rule 2

The total E and M force on a volume of plasma can be computed from surface values through $\vec F = \int \overline{T} \cdot \vec n \dd V$

Rule 3

Magnetic field has a tension and isotropic pressure

$T = \frac{B^2}{\mu_0} \qquad p = \frac{B^2}{2 \mu_0}$

Rule 4

Plasma is frozen in the magnetic field when $\eta = 0$ (zero resistivity).

Rule 5

When $\vec{v}_{mag}$ is the velocity of the magnetic field,

$\vec E = - \vec{v}_{mag} \cross \vec B$

Rule 6

Ambipolar diffusion requires the ions and electrons to leave the plasma at the same rate

$n_{ew} v_{ew} = n_{iw} v_{iw}$

Rule 7

At a given temperature the electron speed is 60 times the D ions requiring a four-e-folding in sheath voltage to make the electron and ion losses equal

$V_{sheath} \approx 4 T_e$

Rule 8

The energy of the ions into the wall is:

$W_{impact} \approx 4 Z_i k T_e + \frac{1}{2} k T_i$

Rule 9

A Langmuir probe can measure $T_e$ $T_i$ and $n$. The probe perturbs the plasma and is good for unmagnetized plasma of $T$ less than $50 eV$ and $n$ less than $10^{20} m^{-3}$ . The probe is used for velocity in magnetized plasma where $v \cross B$ often dominates $E$.

Rule 10

Particles interact within a Debye sphere. Outside $\lambda_D$ distance particles do not see each other due to shielding.

Rule 11: Four collision frequencies

• $\nu_{ei}$ - Electron momentum loss rate on ions. Used in resistivity.
• $\nu_{ee}$ Electron energy exchange rate with electrons. In other words, if you do something to the electrons this is how long it will take to get back to Maxwellian. Same order as $\nu_{ei}$
• $\nu_{ii}$ Ion energy exchange rate with ions
• $\nu_{ie}$ Electron energy exchange rate between electrons and ions. It's about the same as ions slowing down in electrons: $\approx \frac{m_e}{m_i} \nu_{ee}$. For fusion to work, need confinement times longer than this time.

$v_0$