Comparitive Analysis of Laser Efficiency

Yb:FliBe Laser Efficiency Model for BS-Fusion

This concept models a high-efficiency, high-temperature laser system based on ytterbium-doped molten FLiBe (Yb:FliBe), operating at a wavelength of 1050 nm. Ytterbium is a well-established laser dopant known for its:

  • Simple electronic structure
  • Low quantum defect
  • High efficiency and energy storage
  • Long upper-state lifetime (~4× that of neodymium)

Its properties make it ideal for pulsed, high-power lasers operating in extreme environments, such as inside the BS-Fusion reactor.


Laser Energy Flow Breakdown

1. Electrical Input to Laser Diodes

  • Supplied Energy: ~40 MJ
  • Conversion Efficiency (electrical → optical): 50–70%
  • Resulting Diode Output (900–980 nm): 20–28 MJ

2. Absorption by Laser Medium + Quantum Defect

  • Laser Medium: Molten Yb:FliBe
  • Pump Wavelength: ~940 nm
  • Laser Output Wavelength: 1050 nm
  • Quantum Defect Efficiency: ~90% (10% of energy lost as heat)
  • Heat Recovery Assumption: 35% of quantum defect heat reclaimed
  • Net Efficiency After Recovery: ~94%
  • Effective Energy at 1050 nm: 19–26 MJ

3. Optical Amplification & Cavity Losses

  • Amplification: Multi-pass gain through the Yb:FliBe-filled cavity
  • Loss Sources: Scattering, absorption, and imperfect reflectors
  • Raw Optical Losses: ~33%
  • Thermal Recovery Assumption: 35% of those losses reclaimed
  • Net Optical Efficiency: ~79%
  • Final Laser Output at 1050 nm: 15–21 MJ

Summary: Energy Flow

Stage Energy Range (MJ) Efficiency Estimate
Electrical Input 40
Diode Optical Output 20 – 28 50–70%
1050 nm Laser Potential 19 – 26 ~94%
Final 1050 nm Laser Output 15 – 21 ~79%

Overall Efficiency (Electrical → 1050 nm):
~38% – 53%

This approach avoids the inefficient UV-x-ray conversion step used by the National Ignition Facility (NIF), which suffers a ~5% wall-plug-to-target efficiency when converting 1053 nm light to x-rays.


Comparison with Other Fusion Heating Methods

Ohmic Heating (e.g., in Tokamaks):

  • Efficiency: ~100% (initial phase only)
  • Limitations: Ineffective beyond a few keV; requires auxiliary heating

Radio Frequency (RF) Heating:

  • Grid-to-plasma efficiency: ~50%
  • Losses: Occur in power generation, waveguides, antennas

Neutral Beam Injection (NBI):

  • Efficiency: Often <30%
  • Loss Sources: Ion acceleration, neutralization, shine-through
  • ITER projection: ~26% net efficiency, even with negative-ion beams

Conclusion

A heat-capacity laser based on molten Yb:FliBe provides a direct and efficient path to deliver high-energy, long-wavelength laser light to the fusion fuel. With minimal frequency shifting, strong heat recovery assumptions, and the elimination of intermediate conversions, overall efficiencies of 38–53% appear feasible, potentially outperforming traditional magnetic confinement heating methods.

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Rare-earth ions (in molten halide salts) are known to luminesce with measurable absorption/emission features, so a Yb:FLiBe laser is not impossible, but to claim it would operate efficiently at 750 K is doubious.

A neodymium (Nd)-based laser is more likely to maintain a 4-level system at high temperatures (>750 K) than a ytterbium (Yb)-based laser due to fundamental differences in their energy level structures and thermal sensitivities:

:microscope: Key Differences in Energy Level Structures

Nd³⁺ (Neodymium)

  • 4-Level System: Nd lasers typically operate with a 4-level scheme, where the lower laser level is well above the ground state.
  • Thermal Advantage: At high temperatures, the population of the ground state remains low enough that reabsorption from the lower laser level is minimal.
  • Robustness: The energy gap between the laser transition and the ground state is large enough to suppress thermal population of the lower level, preserving efficient lasing.

Yb³⁺ (Ytterbium)

  • Quasi-3-Level System: Yb lasers often operate with a quasi-3-level scheme, where the lower laser level is the ground state or very close to it.
  • Thermal Sensitivity: At elevated temperatures, thermal excitation populates the ground-state manifold significantly, leading to:
    • Hot-band absorption: Increased reabsorption of the emitted laser photons.
    • Multiphonon quenching: Non-radiative decay of the upper laser level due to coupling with lattice vibrations (phonons), especially in molten salt hosts.

:thermometer: High-Temperature Behavior

  • Nd-Based Lasers: More resilient to thermal effects because the lower laser level remains depopulated even at high temperatures, preserving the 4-level dynamics.
  • Yb-Based Lasers: Efficiency drops at high temperatures due to:
    • Increased reabsorption from thermally populated ground-state levels.
    • Reduced upper-state lifetime from multiphonon quenching

:brain: Summary

Feature Nd³⁺ Laser Yb³⁺ Laser
Laser Scheme True 4-level Quasi-3-level
Lower Level Population Low at high T High at high T
Reabsorption Risk Minimal Significant
Multiphonon Quenching Less severe More severe
High-T Efficiency More stable Decreases sharply

So in molten salt or other high-temperature hosts, Nd-based lasers retain their 4-level behavior and efficiency better than Yb-based lasers, which suffer from thermal reabsorption and quenching effects

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OK, assuming we need to hit the target with 10 MJ, the efficiency of a 750 K Nd:FLiBe laser can be estimated:

Reactor Volume and FLiBe Properties

  • Volume=(4\pi/3)(2.5)^3=65.4\space m^3
  • Density \rho_{flibe}=2.09\space g/cc = 2090\space kg/m^3
  • Molecular weight of Li_2F_4Be = 98.9 g/mol.
  • Total moles of FLiBe = 1.38×10^6 moles.

Total Nd ions

  • Assume doping concentration of 0.5 mol%
  • Number of Nd ions = 0.005 × (1.38×10^6) = 6.9×10^3 moles.

Nd Energy Levels and Quantum Defect

  • Assume: pump @ 808 nm, lase @ 1064 nm
  • Photon energy (h \nu) = 6.63×10^{-34} Js * 3×10^8 m/s * 10^9 nm/m * 1/808 nm = 2.46×10^{-19} J
  • Quantum Defect (fraction of energy lost as heat) = (1064-808)/1064 = 0.24

Number of Photons Required for 10 MJ on target

  • Assume: extraction efficiency (\eta) = 30%
  • Applicable Energy per photon = 2.46×10^{-19} J * (1-0.24) * 30% = 5.61×10^{-20} J
  • Number of 808 nm photons pumped = 10×10^6 J / 5.61×10^{-20} J = 1.78×10^{26}

Fraction of Nd ions in inverted population

  • Nd ions = 6.9×10^3 moles * 6.02×10^{23} ions/mole = 4.15×10^{27}
  • Inverted fraction = 1.78×10^{26} / 4.15×10^{27} = 4.3% of 0.5% doped.

Pumping Rate and Upper-State Lifetime

  • Assume optical efficiency for diode laser = 55%
  • Pump optical energy = 1.78×10^{26} * 2.46×10^{-19} J = 43.8 MJ.
  • Pump electrical energy = 43.8 MJ * 100%/55% = 80 MJ.
  • Assume upper-state lifetime = 50 \mu s.
  • Pump power (at 20 \mu s) = 4 TW.
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These might work if the upper-state lifetime can be increased. For example, it takes 125 microseconds to deliver 2 MJ (optical) using 20,000 of these 800 kW laser-diode array modules.

@Fermi Notice the date: 28 April 2015.

2 Likes

@Fermi @Banana

Leonardo manufactures 1.8 MW (optical) laser diode modules with 52% electric-to-optical conversion efficiency. These modules support 500-microsecond pulses and a 50% duty cycle.

In theory, deploying 100,000 of these modules could deliver pulses of 20 MJ—roughly 10× the energy delivered to NIF targets—in 111 microsecond bursts. However, if each module costs more than $10,000, a single BSF power plant would require over a billion dollars’ worth of laser diode hardware. That level of expenditure is totally impractical.

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BSF is a joke—it assumes a rediculous, fatally flawed economic model! Consider the basic fact, which BSF violates: For an economically viable power plant, the cost of construction must be recouped before the plant closes for decommisioning.

Let’s do the math.

BSF Construction Price Tag

Laser diode module: $10,000
Number of modules: 100,000
Subtotal: $1 Billion
If lasers represent half the plant cost: Total = $2 billion

Yearly Energy Production

Target rate: 1 every 15 seconds
Energy per target: 330 MJ
Thermal-to-electric conversion efficiency: 25%
Shots per year: ~32 million
Total energy/year = 1.8*10^14 J

Yearly Revenue

Electricity price $0.13/kWh
Conversion: 1 kWh = 3,600,000 J -> $/J = 3.6E-8 
Total sales (1.8E14 J/yr * 3.6E-8 $/J) = $6.5 million/yr

Payback Time

$2,000,000,000/($6,500,000/yr) = 307 years!

So, it would take a miracle (a BSF power plant would need to run continuously without profit for more than three hundred years) just to break even.

Conclusion: BSF power plants cannot generate profit—they are billion-dollar crypts, entombed beneath layers of molten salt optimism. Anyone foolish enough to begin construction of one should be stopped ASAP. A granite slab should be errected at the site, engraved to display through the centuries: ‘Here lies ROI—sacrificed for optics.’

Ferengi worship profit—it’s their guiding principle, their moral compass, and their cultural identity. Their philosophy is codified in the infamous Rules of Acquisition, a sprawling set of 285 business maxims that govern every transaction and social interaction.

Highest is Rule #1: “Once you have their money, you never give it back.”

In Ferengi economics, if the money borrowed to build a BSF power plant doesn’t need to be repaid for 307 years, it would be a wise acquisition.

That conclusion is as premature as a toddler modeling thermohydraulics in crayon.

While your math easily penitrates the target you chose, its scope is narrower than a collimated neutron beam. You only modeled a single scenario. BSF’s parameter space is vast, uncharted, and riddled with knobs no one’s dared to twist. To draw a general conclusion at such an early and unexplored stage is unjustified.

The way you portrayed BSF, as a necropolis—where capital goes to die, was humorous. However, your analysis was based on several assumptions detrimental to plant performance. Obviously, if the assumptions are bad enough, the payback timeline can be stretched into geological epochs. Instead of focusing on examples with poor efficiency, let’s focus on how to improve the assumptions.

Red’s Assumptions

1. Laser diode modules: $10,000
2. Number of modules: 100,000
3. Target rate: 1 every 15 seconds
4. Energy per target: 330 MJ
5. Thermal-to-electric conversion efficiency: 25%

#1. Future Cost Reduction: Moore’s Law & Learning Curve

The good news is that laser diode costs are expected to plummet with large-scale production and technological improvements – much like semiconductors and solar panels have in the past. Two conceptual models can be used to project future prices under high-volume manufacturing:

  • Moore’s Law Analogy: In the microchip industry, Moore’s Law observed that the number of components (transistors) on a chip doubled roughly every 2 years with minimal cost increase. In practice, this meant cost per function halved with each doubling of technology – an exponential improvement. If a similar trend held for high-power laser diodes, the cost per watt could halve with each doubling of cumulative production. This is an extremely rapid learning rate.
  • 20% Reduction per Doubling (Learning Curve): Many energy technologies follow a more modest learning curve. Swanson’s Law for solar PV is a classic example – solar module prices tend to fall ~20% with each doubling of cumulative output. This corresponds to an “80% learning rate.” Every doubling of production cuts cost to 80% of its previous value. For instance, 20 doublings (~1048576×volume) would reduce cost to about (0.8)^{20}≈0.012 (approximately 1.2% of the original cost). In practical terms, if a module costs $100k in early low-volume production, the price would fall to about $1,200.

This analysis spanned a range from very aggressive improvement (Moore-like) to conservative improvement (20% learning rate). Real-world outcomes could fall in between. Notably, semiconductor lasers are semiconductors, so with large demand, they could start behaving more like mass-produced microchips or LEDs in terms of cost curve. Historical data shows laser diode prices have fallen dramatically as power and efficiency improved. In 2015, state-of-the-art pump diodes for high-energy lasers cost on the order of $5/W; a few years ago this had dropped below $1/W, and roadmaps aim for a few cents per watt in the coming decade. This trend results from improvements in diode efficiency (reducing waste heat hardware), higher output per chip, and automated manufacturing.

#2. Laser Power (+) Shared Amongst Multi-chambers

The drivers are the most expensive components in inertial confinement fusion (ICF) power plants. In a multi-chamber ICF plant, several blast chambers can share one driver system through time-multiplexing. If a laser is used, the driver only needs to pump for a few microseconds, while clearing the chamber between shots takes several seconds. Thus, the laser modules spend most of their potential duty cycle idle in a single-chamber setup. By rotating pulses between many chambers, the same diode array can be kept busy nearly continuously, increasing utilization without exceeding thermal or duty-cycle limits. This means the high capital cost of the driver is spread over many more fusion events per second, lowering the effective cost of the laser per unit of power produced.

The same principle applies to turbines and power conversion systems. When multiple chambers fire in sequence, the combined energy flow into the heat exchangers and turbines becomes smoother and more continuous, allowing the use of larger, shared infrastructure instead of duplicating equipment for each chamber. Large turbines are cheaper per watt and more efficient than many smaller ones, and the balance-of-plant (cooling, piping, generators, grid connection) can also be consolidated. Together, these shared components distribute fixed costs across greater output, so the gigawatts of electricity delivered per dollar invested rise substantially, reducing the plant’s overall cost-per-watt of electricity.

#3. Faster Target Delivery

In Red’s senario, one 330 MJ target gets ignited every 15 seconds. When these targets are fused, their heat energy gets deposited near the ignition site, in coolant at the center of the blast chamber. This heat needs to be exchanged (removed from the blast chamber) by circulating coolant through it. The per shot volume of coolant that needs to be exchanged (inlet → outlet) can be calculated:

V_{\text{per-shot}}=\frac{E}{\Delta T \rho C_p} = 0.2 m^3

where:

  • energy supplied, E = 3.3E8 J
  • temperature swing, \Delta T = 1100-750 => 350 K
  • density, \rho = 2000 kg/m^3
  • specific heat, C_p = 2414 J/kg\cdot K

So, under Red’s assumptions, 0.2 m^3 of coolant would be flowing through the inlet/outlet every 15 seconds (0.8 m^3/\text{minute}). This is two orders of magnitute slower than typical fission reactors, which have volumetric flow rates ranging from 57 to 95 cubic meters per minute.

#4. Higher Yield Targets

#5. Increased Carnot Efficiency

The theoretical maximum efficiency of any heat engine is given by:

η_{\text{Carnot}}=1−\frac{T_{\text{cold}}}{T_{\text{hot}}}

Where, based on molten FLiBe coolant:

  • T_{\text{hot}} = (750-1100) temperature of the working fluid (in Kelvin)
  • T_{\text{cold}} = 300 temperature of the heat sink (in Kelvin)
  • η_{\text{Carnot}} = 60-73%

The following ICF expenses where absent in Red’s analysis, but their inclusion would lower the cost of a power plant based on BSF compared to ICF:

Target Fabrication & Injection: 5-10%
Reaction Chamber & Blanket: 15-25%

But sharing the laser system, and turbines between a large number of multi-chambers would produce the most bang for a given buck.