Questions about UT smoke, lasers, and plasma.

[lwcamp]

Originally Posted by Fred Brackin

Someone who is hoping to stop lasers and/or plasma beams will 1 to 10 hexes of smoke will be probably dropping his smoke grenade near himself and not trying to lay it in front of the firer.

If we want to find out if modern laser weapons can penetrate smoke at tight focus, we will need to run some numbers. We will need to make some approximations to keep the problem practical. First, we can assume that the smoke particle conducts heat within itself much better than air can conduct it away so that the smoke particle rapidly heats up so that all parts of it are at the steady state temperature (if this assumption fails, we might be off by as much as a factor of 2 or 3). Second, we assume that at the smoke particle is small enough that its interaction with the surrounding air is dominated by viscosity - this means we will mostly lose heat via conduction rather than convection. Third, we will assume the smoke particle is spherical - irregular shapes should not change the result much. Fourth, we will assume that the particle absorbs all the light that falls on it. Fifth - and this is the least justified assumption - we will assume that the thermal conductivity of air is independent of temperature, and use the value of thermal conductivity for air at room temperature. In reality, the thermal conductivity of air gets higher as the temperature rises, so the hotter the particle gets the easier it is for heat to be conducted away. Consequently, any estimates we make will be an upper bound to the actual temperature - the real temperature will be lower.

If we have a laser beam with intensity I, a smoke particle of radius R will intercept a power P = 2 pi I R^2. At steady state, the solution to the heat conduction equation for a spherically symmetric source in a uniform bath with asymptotic temperature T0 is T = (P/(4 pi K r)) + T0, where T is the temperature at distance r, P is the power being conducted away through the shell of radius r, and K is the thermal conductivity. At r = R, the temperature T will equal the temperature of the smoke particle, and at steady state the conducted power equals the intercepted radiant power
T = T0 + (2 pi I R^2)/(4 pi K R)
= T0 + (I R)/(2 K).

The higher power modern laser weapons put out about 150 kW. From video footage, they appear to be focused into a spot about 3 cm wide - call it 10 cm^2 in area. This gives I = 1.5E8 W/m^2. The thermal conductivity for room temperature (300 K) air is 0.024 W/(K m). Smoke particles typically range in size from 1E-8 m to 1E-6 m - lets take the geometric average and assume 1E-7 m for our typical smoke particle. T0 is room temperature, or 300 K. Plugging all this in, we find that the smoke particle is heated to a temperature of less than 612 K. This is well below the autoignition temperature for reasonable mostly-already-burned stuff and way below the temperature where there is any significant evaporation, so the 0.1 micron wide particles will not be burnt up or evaporated by the beam. Any smaller particles will be even cooler, and also will be unaffected. Larger particles might end up igniting or even evaporating - plugging in the numbers for the maximum size (1 micron) of smoke particle we get an upper limit temperature of 3400 K. If the smoke particle actually reached this temperature, it would quickly evaporate if it hadn't burnt up. However, as mentioned, it will not get this hot. A lower limit for the temperature can be found by using the thermal conductivity for air at the upper temperature limit (and noting that the thermal conductivity varies as the square root of the temperature), which gives us a final temperature between about 1000 K and 3400 K. So it looks possible that the largest smoke particles could ignite or evaporate - at the very least they should sparkle red, orange, or yellow from their black-body radiation.

So, final result - most of the smoke will not be burnt through by a modern laser weapon at close focus, but a few of the very largest of the smoke particles might get burnt up.

Luke