Closed-book appointment exam · independently graded
Professor — Plasma & Energy Physics. The candidate agent answered from its own knowledge, closed-book; a second, independent examiner agent graded it adversarially.
vaiu-sci-apphys-prof-plasma appointment benchmark (2026-07-16)Closed-book oral exam. Candidate agent adopted the vaiu-sci-apphys-prof-plasma persona (v1.0.0) and answered from its own knowledge; a second, independent examiner agent graded. Condensed candidate transcript below; grading report in vaiu-sci-apphys-prof-plasma-2026-07-16.md.
AI-transparency disclosure. Opened as an AI agent that has never stood at a tokamak or laser bay; closed-book, no tools; names eponyms / flags folklore; no fabricated references; where physics touches real hardware, teaches the physics and refers operations to qualified licensed professionals.
Q1 — What is a plasma. A plasma is an ionized gas showing collective behavior and quasineutrality, earning the name only when (1) λ_D ≪ L, (2) N_D = n·(4/3)πλ_D³ ≫ 1 (many particles per Debye sphere, so screening is statistical), and (3) ω_pe·τ_n ≫ 1 (collective EM beats neutral chemistry). Quasineutrality (n_e ≈ Z n_i) is quasi, not exact — the small imbalances drive the restoring fields — and it fails inside a Debye sphere and in wall sheaths. A test charge is Debye-screened, φ ∝ (1/r)e^(−r/λ_D), with λ_D = √(ε₀ k_B T_e/(n_e e²)) (Debye–Hückel) — the balance of thermal smearing against electrostatic pull. The plasma frequency ω_pe = √(n_e e²/(ε₀ m_e)) depends only on density, not temperature (the plasma's natural "ring," the cutoff below which EM waves reflect). Single-particle motion: gyration at ω_c = qB/m, plus the E×B drift (charge- and mass-independent, drives no current — the cross-field-transport workhorse) and the grad-B and curvature drifts (charge-dependent, drive currents) — in a tokamak, grad-B + curvature separate charges vertically, so a rotational transform (poloidal twist) is needed to short that out, which is why a pure toroidal field cannot confine. Magnetic mirroring: with B slowly varying, the first adiabatic invariant μ = mv⊥²/(2B) is conserved, so entering stronger B raises v⊥² and drains v∥² until reflection (the loss cone escapes) — the Van Allen belts and the magnetic bottle.
Q2 — Kinetic vs fluid. The kinetic description tracks f(x,v,t) in 6-D phase space via the collisionless Vlasov equation ∂f/∂t + v·∇_x f + (q/m)(E+v×B)·∇_v f = 0, self-consistent with Maxwell through f's moments — mandatory whenever velocity-space structure matters (wave-particle resonance, Landau damping, loss-cone/bump-on-tail instabilities, non-Maxwellian tails). Taking moments and combining species gives MHD; ideal MHD (E + v×B = 0, frozen-in flux — Alfvén's theorem) is right for large-scale, low-frequency equilibrium and stability, valid when scales ≫ gyroradius/Debye and the distribution stays near-Maxwellian so the fluid closure is meaningful (the closure being a modeling choice that can fail). Landau damping (Landau 1946) is the canonical collisionless effect: a Langmuir wave damps with no collisions because particles near the phase velocity v_φ exchange energy, and for a Maxwellian there are slightly more particles just slower than v_φ (gaining energy from the wave) than just faster, so with ∂f/∂v < 0 at resonance the wave loses energy. It is not ordinary dissipation — the Vlasov equation is time-reversible and conserves phase-space entropy; the wave energy goes into fine-grained velocity-space filamentation that is in principle reversible (the plasma echo), with true irreversibility entering only when weak collisions smooth that structure. Invert the slope (bump-on-tail) and you get inverse Landau damping — an instability — a sign-sensitivity fluid theory cannot capture.
Q3 — Fusion & the Lawson criterion. The most accessible reaction is D + T → ⁴He (3.5 MeV) + n (14.1 MeV), 17.6 MeV total, favored because its cross-section peaks at the lowest attainable temperature (near ~65 keV, usefully large already at 10–20 keV ≈ 100–200 MK); the charged alpha can stay to heat the plasma (the basis of ignition) while the neutron escapes to a blanket (and drives activation and tritium-breeding). Both nuclei repel via the Coulomb barrier, so fusion happens only by quantum tunneling (the Gamow picture), with the rate dominated by the Gamow peak on the Maxwellian tail. The first-principles cross-section belongs to Physics (see B1); given σ(E), the rate per volume is n_D n_T⟨σv⟩. Net energy requires the fusion power to overcome radiation (bremsstrahlung) and transport losses, giving the Lawson (1957) condition, refined to the triple product n·T·τ_E ≳ ~3×10²¹ keV·s·m⁻³ for D-T ignition. Crucially, n and T are measured data with error bars, while τ_E ≡ W/P_loss and ignition (alpha self-heating sustaining the burn) are inferred. Confinement is the hard part because reaching temperature is easy (>100 MK routine) but holding a hot, instability-prone plasma together long enough (large τ_E) at sufficient n and T simultaneously is defeated by anomalous turbulent transport and abrupt instabilities — which is why the triple product, not any single number, is the honest scorecard.
Q4 — Confinement approaches. Magnetic confinement insulates a hot, low-density (~10²⁰ m⁻³) plasma with strong fields. The tokamak (toroidal + poloidal field, the poloidal field from a toroidal plasma current) supplies the rotational transform; its τ_E is characterized by empirical confinement scalings (e.g. ITER98 H-mode) fit to multi-machine databases — fits and extrapolations, not first-principles guarantees. Its Achilles' heel is disruptions (sudden current termination dumping energy, driving runaway electrons and halo currents); kink (current-driven) and ballooning (pressure-driven) instabilities set the beta and safety-factor limits; and the H-mode (Wagner/ASDEX ~1982) forms an edge pedestal roughly doubling τ_E but bundles in ELMs. The stellarator makes the entire twist with external coils (no plasma current, so steady-state and disruption-free) at the price of 3-D coil geometry and historically worse neoclassical orbits (much improved by optimization). MCF is limited by turbulent cross-field transport (capping τ_E) and MHD stability (capping beta). Inertial confinement takes the opposite corner — compress a tiny D-T capsule so fast that its own inertia holds it for ~tens of picoseconds at thousands of times solid density (driven directly by lasers or indirectly by hohlraum X-rays, ablation rocketing the shell inward to ignite a hot spot). Its killer is the Rayleigh–Taylor instability (a light fluid pushing a heavy one — Rayleigh; G.I. Taylor), amplified by drive non-uniformity, plus Richtmyer–Meshkov at shocks — so symmetry and surface finish are everything, and energy (not a single shot) additionally needs high repetition rate, driver efficiency, and target gain far above the demonstration.
Q5 — Breakeven honesty & energy limits. "Breakeven" and "Q" are inferred quantities, meaningless without a stated boundary: the gain Q = fusion out / some energy in, and which energy in is the whole argument — scientific breakeven (Q_plasma = 1, fusion ≥ energy on target), ignition (alpha self-heating sustains the burn), engineering breakeven (electricity generated ≥ the whole facility's electricity draw), and commercial viability (engineering breakeven + economics). The trap is the denominator: a headline may compare yield to energy on target while ignoring the driver's wall-plug inefficiency — e.g. (illustrative) ~2 MJ on a capsule yielding ~3 MJ is a target-gain Q > 1 and a genuine scientific milestone, while the lasers drew on the order of ~100× that from the wall, nowhere near engineering breakeven. So any Q/breakeven claim must specify: relative to what (on-target vs wall-plug), scientific or engineering, peak or averaged, single-shot or sustained — and even engineering breakeven in a lab is not a power plant (fusion's timeline history counsels humility). A fundamental limit like Carnot (η = 1 − T_C/T_H, a second-law bound you can only approach) or Shockley–Queisser (~33% for a single-junction cell — sub-bandgap loss + thermalization + radiative recombination; multi-junction cells beat the single-junction limit by stacking bandgaps, violating no law) is categorically different from an engineering shortfall that better hardware can reduce.
"Can we build a star on Earth — and why is it so hard?" — novice (the Sun fuses light atoms, and we can do the same reaction, but the Sun has two advantages we can't copy — its crushing gravity and its sheer size — so on Earth we must go hotter than the Sun's core and then hold that gas without it touching a container, and "holding it" is the hard part — hiding that the Sun's power density is low, glossing tunneling, and reducing confinement to a slogan); undergraduate (a star is a self-gravitating plasma in hydrostatic equilibrium fusing via the slow p-p chain; lacking gravity we pick D-T for its lower-temperature peak and must satisfy the Lawson triple product n·T·τ_E simultaneously via magnetic or inertial confinement, fighting turbulent transport and instabilities — treating τ_E as given and not yet separating scientific from engineering breakeven); graduate (a confinement-and-stability problem atop a cross-section we don't control — deriving Lawson from the alpha-heating-vs-loss balance with τ_E ≡ W/P_loss, MCF τ_E set by anomalous gyrokinetic transport with H-mode scalings that are extrapolated fits, the MHD stability spectrum, and ICF's radiation-hydro simulations as model outputs conditioned on their EOS/drive assumptions — with the honest capstone that scientific breakeven ≠ engineering breakeven ≠ a power plant). Each level names what it simplifies.
vaiu-sci-phys-*), while owning the reaction-rate-in-a-plasma side — the Coulomb barrier and why tunneling makes it possible, folding σ(E) against a Maxwellian to get ⟨σv⟩ and the Gamow peak, the volumetric rate n_D n_T⟨σv⟩, and how it feeds the Lawson power balance.Examiner verdict: APPOINT (field 5/5 rubric-correct, 0 fabrications; teaching 3/3; boundary 3/3 including the B2 operational-safety gate). Full report in the sibling result file.