What happens to asteroids when heated into a plasma?

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Asteroid Laser Ablation is a related technique, where a set of lasers heats up part of an asteroid, applying a torque that can change its orbit and (hopefully) send it moving away from Earth. Looking at that might be helpful. Here are some statistics:

Temperatures needed: 3000 K, at the most.¹
Power source for lasers: solar power, possible reaching 50% efficiency¹, or nuclear power^[2].
Power of lasers: 30 kW - 75 kW or more, depending on technological development.^{1, [2]}
Asteroid sublimation temperature: 1700 K.^[2]

This is only to deflect the asteroid, though - not destroy it. We can expand on some of the results, though, using the same models. The second group, Gibbings et al., used an expression for the change in mass of the asteroid, $\dot{m}$: $$\dot{m}=\frac{1}{E}(P-Q_{rad}-Q_{cond})$$ where $E$ is enthalpy, $P$ is the power input, and $Q_{rad}$ and $Q_{cond}$ are the heat losses due to radiation and conduction.

Some rough numbers:

$E=1.97\times10^7\text{ J kg}^{-1}$
$P=75000\text{ J s}^{-1}$
$Q_{rad}=3.79\times10^7\text{ J s}^{-1}$, if the laser bank is focused on 100 square meters of the asteroid at a time.
$Q_{cond}=2.07\times10^{19}\text{ J s}^{-1/2}t^{-1/2}$, where I've used an asteroid density of $\rho=2000\text{ kg m}^{-3}$ and $t$ is the time during which the laser is applied, in seconds.

We see then that $$\dot{m}=\frac{1}{1.97\times10^7}(75000-3.79\times10^7-2.07\times10^{19}\times t^{-1/2})\quad\text{ kg s}^{-1}$$ which is a simple differential equation. If the initial mass of the asteroid is $\sim10^{19}\text{ kg}$, then the solution is, approximately, $$m(t)=10^{19}-1.92005t-2.10152\times10^{12}\sqrt{t}$$

This actually would take quite a while to destroy the whole asteroid; setting $m(t)=0$ suggests it would take $\sim10^{13}\text{ seconds}$ - millennia! Plots from one article about a system support result, give or take: