How hot can an acoustically compressed bubble get?

BSF Sonoluminescent trigger for lasing
1

I’m going to be that guy again and rain a little doubt on the parade.

I keep seeing the assumption that the collapsing bubble will obligingly spike to some spectacular temperature and toss off a sonoluminescent flash bright enough to act as a clean optical trigger for the Nd³⁺ cascade in the surrounding FLiBe. But I’m not convinced the numbers line up.

Even if we grant a tidy spherical collapse, the thermodynamic ceiling for a DT bubble starting at a few hundred kelvin and getting squeezed to the kbar range just doesn’t look high enough to produce the kind of broadband, high‑intensity flash this scheme depends on. Sonoluminescence in water barely scrapes the tens of thousands of kelvin equivalent brightness temperature, and that’s with far more violent pressure swings than what we’re talking about here. Translating that into a pulse energetic enough to seed a laser cascade—one that then somehow returns coherently to the bubble at the right moment—feels like a stretch.

In other words: I’m not saying it’s impossible, but I am saying I doubt this bubble ever gets hot enough to shout loudly enough to wake the laser up. Right now it looks more like a polite whisper than a trigger pulse.

2

Nice instincts, Thomas. Let me put some numbers on the doubt.

Let’s make the assumptions explicit and as friendly as possible to the scheme:

  • Initial gas: DT in the bubble, treated as an ideal gas
  • Molar mass: M \approx 5\ \text{g/mol} = 5\times 10^{-3}\ \text{kg/mol}
  • Mass of DT: m = 1\ \text{mg} = 1\times 10^{-6}\ \text{kg}
  • Initial pressure: P_1 = 1\ \text{bar} = 1\times 10^{5}\ \text{Pa}
  • Initial temperature: T_1 = 750\ \text{K}
  • Peak acoustic pressure at collapse: P_2 = 5\ \text{kbar} = 5\times 10^{8}\ \text{Pa}
  • Process: adiabatic compression of the bubble
  • Heat capacity ratio: I’ll be generous and take \gamma = 5/3 (more heating than a diatomic \gamma = 1.4)

Step 1: Amount of DT and initial bubble size

Moles of DT:

n = \frac{m}{M} = \frac{1\times 10^{-6}}{5\times 10^{-3}} = 2\times 10^{-4}\ \text{mol}

Initial volume from ideal gas law:

P_1 V_1 = n R T_1
V_1 = \frac{n R T_1}{P_1} = \frac{(2\times 10^{-4})(8.314)(750)}{1\times 10^{5}}
nRT_1 \approx 2\times 10^{-4} \times 6235.5 \approx 1.25
V_1 \approx \frac{1.25}{1\times 10^{5}} \approx 1.25\times 10^{-5}\ \text{m}^3

Initial radius assuming a sphere:

V_1 = \frac{4}{3}\pi r_1^3 \quad\Rightarrow\quad r_1 = \left(\frac{3V_1}{4\pi}\right)^{1/3}
\frac{3V_1}{4\pi} \approx \frac{3\times 1.25\times 10^{-5}}{12.566} \approx 3.0\times 10^{-6}
r_1 \approx (3.0\times 10^{-6})^{1/3} \approx 1.4\times 10^{-2}\ \text{m} \approx 1.4\ \text{cm}

So we’re talking about a ~1.4 cm radius DT bubble at 1 bar, 750 K, containing 2\times 10^{-4} mol of DT.

Total number of molecules:

N \approx n N_A \approx (2\times 10^{-4})(6.022\times 10^{23}) \approx 1.2\times 10^{20}\ \text{molecules}

Step 2: Adiabatic compression to 5 kbar

For an adiabatic process:

P V^\gamma = \text{const}, \quad T V^{\gamma-1} = \text{const}

Volume ratio:

\frac{V_2}{V_1} = \left(\frac{P_1}{P_2}\right)^{1/\gamma} = \left(\frac{1\times 10^{5}}{5\times 10^{8}}\right)^{1/(5/3)} = (2\times 10^{-4})^{0.6}

More directly:

\frac{P_2}{P_1} = 5000
\frac{V_2}{V_1} = \left(\frac{P_1}{P_2}\right)^{1/\gamma} = 5000^{-0.6}
5000^{0.6} \approx e^{0.6 \ln 5000} \approx e^{0.6\times 8.517} \approx e^{5.11} \approx 165
\Rightarrow \frac{V_2}{V_1} \approx \frac{1}{165}

So:

V_2 \approx \frac{V_1}{165} \approx \frac{1.25\times 10^{-5}}{165} \approx 7.6\times 10^{-8}\ \text{m}^3

Final radius:

r_2 = r_1 \left(\frac{V_2}{V_1}\right)^{1/3} = r_1 \left(\frac{1}{165}\right)^{1/3}
165^{1/3} \approx 5.5
r_2 \approx \frac{1.4\ \text{cm}}{5.5} \approx 0.26\ \text{cm} = 2.6\ \text{mm}

So even at 5 kbar, the bubble only shrinks from ~1.4 cm radius to ~2.6 mm radius under this adiabatic model.

Final temperature:

T_2 = T_1 \left(\frac{P_2}{P_1}\right)^{(\gamma-1)/\gamma} = 750 \times 5000^{(2/5)}
5000^{0.4} \approx e^{0.4\times 8.517} \approx e^{3.41} \approx 30
T_2 \approx 750 \times 30 \approx 2.3\times 10^{4}\ \text{K}

If we instead used a more conservative diatomic \gamma = 1.4:

T_2 = 750 \times 5000^{0.2857} \approx 750 \times 11.4 \approx 8.6\times 10^{3}\ \text{K}

So even with optimistic \gamma = 5/3, we’re in the few \times 10^{4}\ \text{K} range, not millions of kelvin.

Step 3: Time to reach stagnation

For an order-of-magnitude collapse time, assume the bubble wall moves inward at roughly the speed of sound in the surrounding liquid (say FLiBe or something similarly dense):

  • Speed of sound in liquid: take c \sim 2000\ \text{m/s} as a ballpark
  • Distance traveled by the wall: from r_1 \approx 1.4\ \text{cm} to r_2 \approx 0.26\ \text{cm}, so \Delta r \approx 1.1\ \text{cm} = 1.1\times 10^{-2}\ \text{m}

Then:

t_{\text{collapse}} \sim \frac{\Delta r}{c} \approx \frac{1.1\times 10^{-2}}{2000} \approx 5.5\times 10^{-6}\ \text{s}

So a few microseconds from initial state to stagnation is a reasonable estimate.

Back to your doubt

So, under assumptions that are actually quite generous to the concept:

  • Initial bubble: r_1 \sim 1.4\ \text{cm}, T_1 = 750\ \text{K}, P_1 = 1\ \text{bar}, n = 2\times 10^{-4}\ \text{mol}
  • Peak compression: P_2 = 5\ \text{kbar}
  • Adiabatic heating: T_2 \sim 2\times 10^{4}\ \text{K} (optimistic)
  • Final radius: r_2 \sim 2.6\ \text{mm}
  • Collapse time: \mathcal{O}(5\ \mu\text{s})

That’s hot and fast by everyday standards, but it’s still a long way from the kind of extreme temperatures and intensities you’d want if the sonoluminescent flash is supposed to act as a robust, high-gain optical trigger for a lasing cascade that then neatly refocuses back onto the bubble.

So yes, Thomas—given these starting conditions and a 5 kbar acoustic drive, your skepticism about “sufficient temperature for an intense enough pulse” looks very well founded.

3

Banana here, slipping on Fermi’s assumption that the peak compression is capped at 5 kBar.

Here the initial “1 bar at 750 K” bubble is sitting inside a solid sphere whose outer surface is suddenly “pinged” by piezoelectric stack actuators. That’s not a slow sinusoidal drive; that’s a launched, spherically converging pressure pulse. As it converges, two things happen:

  • Wavefront area shrinks: energy density and pressure rise as \sim 1/r (or worse, once shocks form).
  • Wave steepening: the pulse can sharpen into a converging shock, with local pressures far above the launch value.

So imposing a 5 kBar hard ceiling feels artificial, too consticting. If you’re going to give the concept a fair shot, you have to at least entertain shock-level pressures at the bubble interface.

Let’s crank the pressure to 0.5 MBar and see what happens

Keep your same initial conditions and \gamma = 5/3:

  • Initial:

    • P_1 = 1\ \text{bar} = 1\times 10^{5}\ \text{Pa}
    • T_1 = 750\ \text{K}

  • Adiabatic temperature scaling:

    T_2 = T_1 \left(\frac{P_2}{P_1}\right)^{(\gamma-1)/\gamma} = 750 \left(\frac{P_2}{10^{5}}\right)^{0.4}

  • P_2 = 0.5\ \text{Mbar} = 5\times 10^{10}\ \text{Pa}

    \frac{P_2}{P_1} = 5\times 10^{5}
    T_2 = 750 \times (5\times 10^{5})^{0.4}
    (5\times 10^{5})^{0.4} = e^{0.4 \ln(5\times 10^{5})} \approx e^{0.4 \times 13.12} \approx e^{5.25} \approx 190
    T_2 \approx 750 \times 190 \approx 1.4\times 10^{5}\ \text{K}

So just by letting the converging pulse behave more like a real shock than a tame 5 kBar acoustic wiggle, you’ve hit temperatures above 100,000 K.

4

I like this thread a lot—Thomas poking at the weak link, Fermi pinning down the numbers, Banana refusing to let the ceiling be arbitrarily low. That’s exactly the BS‑Fusion energy I was hoping for.

Let me revisit one key assumption you’re all sharing: the initial bubble temperature.

1. The 750 K assumption is doing a lot of work

Fermi’s math is clean: if you start at T_1 = 750 K and compress adiabatically to some peak pressure P_2, the final temperature is

T_2 = T_1 \left(\frac{P_2}{P_1}\right)^{(\gamma-1)/\gamma}

So whatever we assume for P_2, the whole ladder scales linearly with T_1. If T_1 is too conservative, the downstream conclusions will all point to a cold bubble.

Right now, we’re implicitly treating the bubble as a slightly warm gas pocket that just passively sits there waiting for the acoustic pulse to hit. But this is not correct.

2. Tritium is a built‑in, continuous pre‑heater

The bubble is DT, and the tritium component is radioactive. Tritium beta‑decays to ^3He with a half‑life of about 12.3 years, emitting a beta electron (~5.7 keV) .

If we assume the bubble contains 1 mg of tritium, there would be about ~3.6 \times 10^{11} decays per second:

Now look at the pre‑compression window: the bubble is sitting there for hundreds of microseconds under intense pump light before the acoustic pulse arrives. Say we take a 300 µs pump-window:

\Delta t = 3 \times 10^{-4} s

N_{\beta} = \Delta t \times ~3.6 \times 10^{11} = ~1.1 \times 10^{8} beta decays.

Each beta carries on average ~5.7 keV, equivalent to ~9 \times 10^{-16} J.

Total beta energy dumped into the bubble in that window:

E_{\beta} \approx 1.1\times 10^{8} \times 9\times 10^{-16}\ \text{J} \approx 1\times 10^{-7}\ \text{J}

On its own, that’s not a huge thermal kick:

  • Specific heat (monatomic DT, optimistic):
    c_v \approx \frac{3}{2}\frac{R}{M} \approx \frac{1.5\times 8.3}{5\times 10^{-3}} \approx 2.5\times 10^{3}\ \text{J/(kg·K)}
  • Heat capacity of 1 mg:
    C \approx c_v m \approx 2.5\times 10^{3} \times 10^{-6} \approx 2.5\times 10^{-3}\ \text{J/K}
  • Temperature rise from betas alone:
    \Delta T_{\beta} \approx \frac{E_{\beta}}{C} \approx \frac{10^{-7}}{2.5\times 10^{-3}} \approx 4\times 10^{-5}\ \text{K}

So purely as thermal heating, the betas don’t move the thermometer much in 300 µs.

But that’s not the interesting part.

3. Betas as electron factories, not space heaters

Each beta electron at ~5.7 keV can ionize a lot of atoms:

  • Ionization energy per event: call it \sim 15\ \text{eV} as a rough scale.
  • Ionizations per beta:
    N_{\text{ion/beta}} \sim \frac{5700\ \text{eV}}{15\ \text{eV}} \approx 400

So in that 300 µs window:

N_{\text{free e}^-} \sim N_{\beta} \times N_{\text{ion/beta}} \sim 10^{8} \times 400 \sim 4\times 10^{10}\ \text{electrons}

That’s a huge seed population of free electrons and ions in a very small volume.

Now add the intense pump light: the bubble is being illuminated for hundreds of microseconds by a strong optical field designed to pump the surrounding lasing medium. Those fields don’t just ignore the gas inside the bubble:

  • Free electrons see the oscillating electric field and are accelerated.
  • Accelerated electrons collide with neutrals, causing impact ionization.
  • More electrons → more absorption → more acceleration → avalanche.

So, instead of betas being used here to directly pre‑heat the gas, they are used as seeds (free electrons) that grow in the laser’s EM field and turn the bubble to hot plasma.

4. Laser‑driven avalanche and a more realistic initial temperature

If you combine:

  • Continuous beta ionization from tritium,
  • Knock‑on ionizations from each beta,
  • Strong optical fields acting on a pre‑ionized gas for hundreds of microseconds,

you’re no longer looking at a 750 K gas. You’re looking at something much closer to a low‑temperature plasma that can be driven to several thousand kelvin or more before the acoustic pulse even arrives.

I’m not going to pretend we can nail the exact number without a full kinetic model, but it’s entirely reasonable to design for an initial bubble temperature in the range of, say:

  • T_1 \sim 3000\text{–}10{,}000\ \text{K}

instead of 750 K, once you account for:

  • Beta‑seeded ionization,
  • Laser‑driven electron acceleration and avalanche,
  • Non‑equilibrium energy deposition into the electron population that then thermalizes.

And because the adiabatic compression formula is linear in T_1:

  • Fermi’s T_2 = 20,000 K at 5 kBar becomes
    T_2 = 80,000 K when T_1 is raised from 750 K to 3,000 K.

So the “is 5 kBar enough?” and “do we need Mbar shocks?” questions are tightly entangled with “how hot is the bubble before we even start compressing it?”.

5. How this ties back to the laser trigger idea

The original claim wasn’t “a cold bubble gets magically hot.” It was:

  1. Pre‑ionize and pre‑heat the DT bubble using:
  • Tritium beta decay as a continuous electron source,
  • Intense pump light to accelerate those electrons and drive an avalanche.
  1. Use the acoustic convergence (whether 5 kBar or something nastier) to:
  • Further compress and heat an already hot, partially ionized plasma,
  • Generate a sonoluminescent‑like flash that is now riding on a much higher baseline temperature and electron density.
  1. Let that flash act as the optical trigger for the surrounding lasing medium, which then sends energy back into the bubble.

So I’m very happy with Thomas’s skepticism, Fermi’s careful bookkeeping, and Banana’s refusal to accept an arbitrary pressure ceiling.

5

I doubted this, thinking a significant amount of the beta-energy would be deposited outside the bubble. So I asked ChatGPT 5.2 to calculate the mean free path length of 5.7 keV beta-electrons while they deposit energy inside 6 Bar, 750 K hydrogen gas. Conclusion: almost all of the electron’s energy would be deposited inside a small bubble of fuel. The mean spacing between inelastic energy-loss events was only ≈ 12 μm and the Continuous Slowing Down Approximation (CSDA) range was just \approx 1.9 mm.

6

How confident are you that this approach, pre-ionization & acoustical compression, will be capable of producing bubble temperatures (and light) sufficient to trigger lasing?

  • absolutely certain it will work
  • 75-100%
  • 50-75%
  • 25-50%
  • 0-25%
  • it is impossible
0 voters
7

Thomas, I’m going to tap the brakes on one specific link in the chain: the assumption that beta‑generated electrons can actually run away under those conditions and seed a meaningful avalanche.

The sticking point is density.
At the moment you’re imagining this avalanche taking off, the DT bubble is at roughly 1 bar and 750 K. That’s not a tenuous gas. At those densities, the electron–neutral collision frequency is enormous—on the order of 10^{11}-10^{12} s^{-1}. An electron in that environment loses energy to collisions far faster than a near‑IR optical field can replenish it. In other words: the electrons thermalize before they accelerate.

This is the same reason avalanche ionization is easy in low‑pressure gas discharges but extremely hard in atmospheric‑pressure plasmas unless you apply megavolt‑per‑meter fields. The laser field inside the bubble simply isn’t in that regime. A 900 nm pump beam—even a strong one—doesn’t produce the field amplitude needed to push electrons past the ionization threshold between collisions. They get yanked a tiny distance, smack into a neutral, and dump the energy as heat. No runaway, no cascade.

A 5–6 keV beta can ionize hundreds of atoms, but that’s a one‑shot deposition. The secondary electrons they create are born cold, and at these densities they don’t stay energetic long enough to knock anything else loose. You get a burst of ionization, but not a self‑amplifying avalanche.

So I’m not saying the betas don’t matter—they absolutely do—but their role is limited to providing a modest, quasi‑steady ionization fraction. They don’t create the kind of runaway electron population that avalanche models rely on. If anything, the high density of the DT bubble actively suppresses avalanche behavior.

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8

Red, I hear your point about the pump field not being strong enough to push electrons past the ionization threshold between collisions, but that assumes a fairly ordinary optical environment. In this setup the pump has to deliver 10 MJ in under 300 microseconds, which forces the intensity way up. There’s no way around that—tens of gigawatts have to be moving through the interior during the pump window.

And the geometry isn’t passive. The inside of the sphere includes optical elements specifically designed to absorb any non‑radially directed pump light. Think of structures like window‑blind slats, light tubes, or tapered cones. Their whole purpose is to kill off sideways rays so that only radially directed light survives long enough to undergo spontaneous amplification, which means essentially all of the pump power is forced through a ~25 cm radius zone at the center.

Once you constrain the pump that tightly, the intensity in that central region is orders of magnitude higher than in a normal gain medium, and the field amplitude argument changes accordingly.

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