ANULUM / SCPN Reactor Systems / Magneto-inertial and magnetised-target systems / Physics

The physics of magneto-inertial compression

Magneto-inertial fusion compresses a magnetised target on inertial time-scales. The embedded field does not hold the plasma the way a tokamak's field does; it lengthens the path heat must take to leave the fuel while a liner, a jet shell or a colliding plasmoid does the compressing. This page collects the closed-form relations the four device cores of the family evaluate, in the order a shot happens: the drive, the compression, and what the ideal relations leave out.

What these relations are. Every relation on this page is one a device core of this family implements as a closed-form evaluation on a declared operating point at computational_prototype maturity. The compression laws are conservation laws in their ideal limit: a real liner has finite conductivity and loses flux, a real compression radiates and conducts. They are therefore upper bounds, never predictions. No equation of motion, equation of state or transport equation is solved here; no yield, gain, reactivity, confinement or breakeven statement is made; no value describes or validates any real machine.

1 · Where the regime sits

Magnetic confinement holds a low-density plasma for seconds with a field it never lets go of. Inertial confinement compresses a dense target so fast that its own inertia holds it together for the nanoseconds of the burn. Magneto-inertial fusion takes the middle: a target that is already magnetised is compressed by a driver on the microsecond to nanosecond scale, and the field, compressed with it, slows thermal conduction out of the fuel. Density and time-scale sit between the two classical regimes, which is why the four configurations of this family can look so different — a pulsed-power liner, a rotating liquid metal, thirty plasma guns, two colliding compact toroids — and still share one set of governing relations.

2 · The drive

Field and pressure at the liner surface (MagLIF)

An axial current $I$ through a cylindrical liner of radius $r$ puts an azimuthal field at its surface, and that field carries a magnetic pressure:

$$B_\theta(r) = \frac{\mu_0 I}{2\pi r}, \qquad p_{\mathrm{mag}} = \frac{B^2}{2\mu_0}$$The vacuum field of an axial current at the liner surface. No circuit, no current distribution and no instability is modelled. (SCPN-MIF-MAGLIF-CORE, level-0 device physics.)

Liner mass and implosion energy (material liner, MagLIF)

A liner is declared from the outside in: inner radius $r$, wall thickness $d$, length $l$, material density $\rho$. Its mass is the exact annulus, not the thin-shell approximation; the two differ by a fraction $d/(2r+d)$, which is 0.74 % at the filed Los Alamos design point and comparable to the tolerance the energy anchor is asserted at, so it is not discarded.

$$m = \rho\,\pi\left[(r+d)^2 - r^2\right] l, \qquad E_{\mathrm{kin}} = \tfrac{1}{2} m v^2, \qquad \tau = \frac{r_0}{v}$$$\tau$ is the time the shell needs to cross its own initial radius at the declared velocity: a scale, not a trajectory, because a real implosion accelerates. (SCPN-MIF-LINER-CORE; the same mass and energy relations in SCPN-MIF-MAGLIF-CORE.)

Preheat (MagLIF)

The second MagLIF stage deposits laser energy $E_{\mathrm{pre}}$ into the fuel column the bore encloses. The core records the energy per unit fuel volume:

$$u_{\mathrm{pre}} = \frac{E_{\mathrm{pre}}}{\pi r_{\mathrm{bore}}^2\, h}$$Deposited energy divided by the enclosed fuel volume; coupling efficiency is a declared input, not a modelled quantity.

A liner made of jets (plasma-jet MIF)

An array of $N$ plasma guns on a launch sphere of radius $R$ fires jets of radius $r_j$, speed $v$ and total mass $M$. Each jet subtends a half-angle at the centre; the caps add up to a fraction of the sphere; the liner the jets are meant to form has a shell density and a ram pressure:

$$\alpha = \arcsin\frac{r_j}{R}, \qquad f_{\mathrm{cap}} = N\,\frac{1-\cos\alpha}{2}, \qquad \rho_{\mathrm{shell}} = \frac{M}{4\pi R^2 \cdot 2 r_j}, \qquad p_{\mathrm{ram}} = \rho v^2$$$f_{\mathrm{cap}}$ is a sum of cap areas, not a coverage map: caps cannot tile a sphere, so a value above one means overlap somewhere and says nothing about whether any point is left bare. The merging of discrete jets into a liner is the subject of the filed source and is not modelled. (SCPN-MIF-PLASMA-JET-CORE.)

3 · The compression

Once the liner converges by a ratio $C = r_0/r$, three ideal conservation laws bound what happens to the enclosed field, density and temperature. The exponent depends on the geometry, and that difference is the reason the plasma-jet core writes its own relations rather than borrowing the cylindrical ones.

Cylindrical liner (MagLIF, material liner, FRC in a theta-pinch coil)

$$B_z = B_{z0}\,C^{2}, \qquad n = n_0\,C^{2}, \qquad T = T_0\,C^{\,2(\gamma-1)}$$Axial flux $B_z \pi r^2$ conserved (perfect-conductor limit); particles per unit length conserved; adiabatic heating with $T \propto n^{\gamma-1}$. At $\gamma = 5/3$ the temperature exponent is $4/3$.

Spherical liner (plasma jets)

$$n = n_0\,C^{3}, \qquad T = T_0\,C^{\,3(\gamma-1)}$$The gain is the volume ratio. At $\gamma = 5/3$ the temperature exponent is exactly 2. The plasma-jet core records density and temperature only; it does not model the field.

What the ideal laws imply for pressure and beta

Combining the cylindrical relations, the thermal pressure $p = nk_BT$ grows as $C^{2+2(\gamma-1)} = C^{10/3}$ while the magnetic pressure grows as $C^4$. Their ratio, the plasma beta, therefore falls as $C^{-2/3}$ under ideal cylindrical compression: the field gains on the plasma. This is a consequence of the same three laws, stated here for orientation; the cores do not record beta.

4 · What the ideal laws leave out

The relations above are ceilings. Three of the losses that lower them are named explicitly in the family's own repositories, with the solver that carries them living in SCPN-Fusion-Core, never in a device core:

Finite conductivity. A real liner and a real plasma lose flux. SCPN-Fusion-Core carries a non-adiabatic flux evolution $\mathrm{d}\psi/\mathrm{d}t = -\psi/\tau_\psi + R_{\mathrm{null}} E_\theta - \eta_{\mathrm{Spitzer}} J_\theta$ after Ono et al. 1997.
Radiation and conduction. The adiabatic exponent assumes no heat leaves. The embedded field slows conduction; it does not stop it, and it does nothing for radiation.
Magneto-Rayleigh–Taylor instability. A decelerating or accelerating liner–plasma interface grows ripples; the family's MagLIF core budgets it as device truth, and SCPN-Fusion-Core carries the growth rate $\gamma(k,a_{\mathrm{eff}}) = \sqrt{k a_{\mathrm{eff}} - k^2 B_\perp^2/(\mu_0 \rho)}$ after Velikovich et al. 2007.
Jet merging. Whether thirty jets become one liner is a question the filed plasma-jet source studies; the core reports the cap sum and stops.

5 · The target: a field-reversed configuration

Two of the four configurations compress a compact toroid, and the FRC is the target the group's own SCPN-FRC-CORE describes. Its level-0 physics is radial pressure balance and an empirical bound on kinetic scale:

$$p_{\max} = \frac{B_e^2}{2\mu_0}, \qquad \langle\beta\rangle = 1 - \frac{x_s^2}{2}, \qquad S^* = \frac{r_s}{\delta_i},\; \delta_i = \frac{c}{\omega_{pi}}, \qquad E = \frac{l_s}{2 r_s}, \qquad \frac{S^*}{E} < 3.5$$An FRC is held by a poloidal field alone; the plasma pressure at the null carries the whole external magnetic pressure. $x_s$ is the separatrix radius over the coil radius. The bound 3.5 is the empirical value printed by Bala et al. (arXiv:2204.07978, eq. 14); a configuration inside it is ordered, not claimed stable.

The FRC-compression configuration adds the kinematics of two counter-propagating plasmoids that must arrive at the chamber centre phase-locked. SCPN-MIF-Core writes them as a Doppler-corrected, distance-coupled Kuramoto pair, a chamber-fixed moving frame and a merge-window monitor:

$$\dot\theta_i = \omega_i + \frac{K_{ij}}{1 + |z_i - z_j|/L_z}\,\sin(\theta_j - \theta_i - \alpha) + D\,\frac{v_{zi} - v_{zj}}{\tfrac12(|v_{zi}| + |v_{zj}|) + \varepsilon_v}$$Lock when the maximum circular phase separation is below 0.01 rad and every plasmoid is within 2 mm of the reference for three consecutive samples. The declared targets are a sensor-to-actuator latency below 50 ns, merging at or above Mach 1 ($v_z \ge 300$ km/s) and a 20 T compression peak field; the sub-50-ns budget is not established on silicon. See FRC compression.

Continue

Explorer

Move the convergence ratio and the drive inputs; every output is labelled as the ideal limit it is.

The four configurations

What each core owns, excludes and anchors on a printed source.

Sources

The filed reports and papers behind every number on these pages.