375. Inertial confinement: concluding part on lasers

Posted by Dmitry

April 28, 2009

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The previous parts on interaction between laser emission and material of fuel capsule are “Inertial confinement – using lasers for compression” and “Inertial confinement: more on interaction of laser emission with matter“. I hope to finish with discussion of laser-target interaction today and proceed to instabilities (the most interesting part of the physics of inertial confinement reactors from my point of view).

So, as we discussed previous time, the outer shell of the capsule (ablator) rapidly evaporates due to the interaction with laser emission. A so called ablative pressure impulse is formed near the boundary of the evaporating region: the main contribution into this pressure comes from heat pressure and reactive pressure of plasma (if plasma temperature is around 1 keV, plasma moves towards the center of the capsule with characteristic velocities as high as $\approx 300 {\rm km}/{\rm s}$ , corresponding to reactive pressure around 10^6 atm).

Due to ablative pressure the part of the capsule that did not evaporate is getting collapsed towards the center of the capsule (typically, the characteristic time of collapse is of the same order of magnitude as the length of the laser impulse). The collapse itself can be described as follows.

Let us consider for simplicity that the target (fuel capsule) is almost a sphere, with thin ablator (outer layer) and empty inside. If so, we can write

$M\frac{du}{dt}=4\pi{}R^22\rho{}v^2$ , (1)

$\frac{dM}{dt}=-4\pi{}R^2\rho{}v$ , (2)

where $M=4\pi{}R^2\delta{}R\rho_0$ is the mass of abalator layer, – “current radius” of the compressed target, – is the compression velocity and is the velocity of target corona. The solution of the Eqs. (1) and (2) depends only on a single parameter

$\beta=\frac{\rho{}R}{\Delta{}R\rho_0}$ .

The compression velocity (it is of the same order of magnitude as the speed of sound in plasma) and kinetic energy of the ablator Mu^2/2 are other two important parameters.

One more important parameter is a quantity

$\gamma=\frac{Mu^2}{2\int{}Qdt}$

called hydrodynamic efficiency. It determines how much absorbed energy goes into kinetic energy of collapsing ablator layer. In spherical targets, $\gamma$ depends on $\beta$ and varies from 3% to 15%.

Rayliegh-Taylor instabilities in fuel capsule

Rayleigh-Taylor instabilities in fuel capsule. Computer simulations by LLNL.

Apart from transformation of absorbed energy and kinetic energy of collapsing ablator (the outer layer acts as a forcer adiabatically compressing the fuel inside the capsule), there is another important mechanism that leads to compression of the fuel – shock waves. Simultaneously, shock waves are the big problem for the whole idea since they lead to inhomogeneous heating of the fuel. Fast electrons created due to the interaction of target material with the laser impulse and X-rays as well as development of Rayleigh-Taylor instabilities also lead to inhomogeneous heating of the fuel. In overall, we do have freedom to resolve these issues to some extent since we can set the flux in the laser impulse ( $10^{14}-10^{16}\frac{\rm W}{{\rm cm}^2}$ ), its wavelength ( $(0.3-0.6)\times{}10^{-6}{\rm m}$ ), the form of the impulse and the capsule.

If we are able to relatively precisely control the form of the capsule and the homogeneity of the laser impulse, theory shows that the peripheral part of the target can be compressed up to the densities of the order $10^2-10^3 \frac{\rm g}{{\rm cm}^3}$ and temperatures around 0.5-1 keV, while the central part of the capsule can be heated up to 10 keV (the density there will be much smaller though – about $5-50\frac{\rm g}{{\rm cm}^3}$ ). In principle, this is enough for a self-sustained thermonuclear reaction to take off. The reaction will start in the center of the capsule and capture the outer layers of the target.

Entered Apprentice, Nuclear physics

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365. Inertial confinement – using lasers for compression

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