TOPIC 1 - Magnetic Confinement Fusion

C: Conceptual, D: Able to Derive, U: Able to use

C: How is the charged particle confined?

Charged particles in magnetic confinement fusion are confined using strong magnetic fields that create a toroidal or stellarator shapes.

C: Why is the toroidal field alone not a sufficient solution?

The toroidal field alone is not sufficient because it does not provide stability against particle drift and can allow some charged particles to escape.

C: Rotational Transform and safety factor

The rotational transform is a measure of the twist of magnetic field lines in a plasma, and it helps define the safety factor, which determines how well the magnetic configuration can confine the plasma and prevent instabilities. - Helical path.

D: Relationship between safety factor q and the angle l

q = #turns toroidally/ poloidal turn = 2pi/l

C: How is current driven in a tokamak?

Transformer Action

C: Gain Factor, Q and what is engineering Q?

Q = (P_out - P_in )/ P_in = (P_n+P_alpha) / P_ext = P_fusion / P_ext

Q = 0; no fusion. Q = 5; burning plasma regime. Q=10;ITER. Q to infinity at ignition.

Q enginerring is for electrical power and is always less than Q. The engineering Q for ITER is around 2.

Power Balance

Confinement time tau_E

tau_E = W / P_L where P_L is the - change in stored energy W

P-bremmstrahlung proportionalities and Z-effective

P_br = const Z² n_i n_e T^1/2

Z-eff = 1/n_e \sum n_j Z_j²

Lawson Criteria

nT \tau_E > 3×10²¹ m-3 KeV s

n \tau_E > 12T/(<ov>E_alpha )

Magnetic Moment Expression

mu = mv_perp² / 2B is an adiabatic invarirent

When is a particle lost? - Magnetic Mirror

Magnetic Mirror Trapping Condition Derivation

Loss Cone

The loss cone refers to a region in velocity space of plasma particles where their motion leads to escape from confinement due to magnetic field gradients, particularly in magnetically controlled environments.

Grad B Drift Velocity

V-gradB = mv_perp² /2qB³ (B X gradB)

Curvature Drift Velocity

V-R = mv_parallel² /qB³ (B X gradB)

Consequence of grad B and curvature drifts

Drifts are charge dependent → Ions and electrons drift in opposite direction → E-field → EXB /B² drift produced that is parallel to R, so the particles are lost in the walls

FIX: Add polloidal field