Design and mechanical analysis of the PRAGYA tokamak vacuum vessel

This paper presents the final design and a comprehensive 3D finite element structural analysis of the PRAGYA tokamak's vacuum vessel, confirming that its distinctive features and robust construction can safely withstand self-weight, atmospheric pressure, and thermal stresses during operation.

The Gist

Imagine you are trying to build a tiny, super-hot star inside a machine on Earth. This machine is called a tokamak, and the specific one described in this paper is named PRAGYA. It's India's first privately built tokamak, designed by a company called Pranos Fusion Energy.

Think of PRAGYA as a high-tech, miniature solar system where we try to trap super-hot gas (plasma) using powerful magnets so it doesn't touch the walls and melt everything.

Here is the simple breakdown of what the paper is about, using everyday analogies:

1. The Big Picture: What is PRAGYA?

PRAGYA is a "low aspect ratio" tokamak. That's a fancy way of saying it's shaped like a fat donut rather than a thin bagel.

• Why a fat donut? In the world of fusion, a fat donut shape is actually more stable and efficient for holding the energy, kind of like how a fat tire on a bike is more stable than a skinny one.
• The Goal: It's a "test bed." It's not going to power a city yet. Instead, it's a training ground to teach engineers how to build bigger, better fusion reactors in the future.

2. The Star of the Show: The Vacuum Vessel

The paper focuses entirely on the Vacuum Vessel. Think of this as the strong, airtight glass jar that holds the star.

• The Job: It has to hold a vacuum (no air) so the plasma can exist, while also withstanding the weight of the machine, the heat, and the magnetic forces.
• The Material: It's made of Stainless Steel 304L. Think of this as the "kitchen-grade" steel you might find in a high-end sink, but super-strong and non-magnetic.

3. The Clever Design Tricks

The engineers had to solve some tricky problems to make this jar work. Here are their solutions:

• The "Electrical Break" (The Speed Bump):

  • The Problem: When the magnetic fields change, they can induce electricity (eddy currents) in the metal walls of the jar. This is like shaking a metal bucket and creating sparks that mess up the star inside.
  • The Fix: They cut the donut jar in half and put a plastic insulator (G10) between the two halves. It's like putting a rubber gasket between two metal pipes. This stops the electricity from flowing all the way around the circle, keeping the magnetic fields calm.

• The "Double O-Ring" (The Double Lock):

  • The Problem: If air leaks into the jar, the star dies.
  • The Fix: Instead of just one rubber seal (O-ring) where the two halves meet, they used two. They even pump the space between the two rings down to a vacuum.
  • The Analogy: Imagine a double-door airlock in a submarine. If the outer door leaks, the air gets stuck in the middle chamber and is pumped out before it can reach the inside. This ensures a perfect seal.

• The "Ribcage" (Stiffeners):

  • The Problem: The jar is thin (only 6mm thick) to save space, but thin metal bends easily under pressure.
  • The Fix: They added internal metal ribs (stiffeners) running along the inside, like the ribs in a human chest or the ribs inside a suitcase.
  • The Result: These ribs make the thin metal incredibly strong. The paper says adding them reduced the stress on the metal by 6 to 7 times. Without them, the jar would need to be much thicker and heavier.

4. The Stress Test: "Will it Break?"

The authors didn't just draw the design; they ran massive computer simulations (like a video game physics engine) to see if the jar would break under pressure. They tested three main scenarios:

1. The Squeeze (Vacuum vs. Atmosphere): The jar is empty inside (vacuum) but the air outside is pushing in with the weight of the atmosphere.

   • Result: The jar held up perfectly. The most it bent was about 0.5 mm (less than the width of a pencil eraser).

2. The Oven (Baking): Before starting, the machine needs to be "baked" at 150°C (300°F) to dry out any moisture stuck to the metal walls.

   • The Problem: Heating metal makes it expand. If it expands unevenly, it can crack or warp.
   • Result: The computer showed the metal got hot and expanded, but the design allowed for this movement. The stress was high, but still within the "safe zone" for the steel.

3. The Wobble (Buckling): They checked if the legs holding the jar would collapse under the weight.

   • Result: The legs are incredibly strong. The analysis showed they could hold 120 times the weight of the machine before they would even think about buckling.

5. The Ports (The Windows and Doors)

The jar has 22 different holes (ports) for cameras, gas injectors, and pumps.

• The Challenge: Holes are weak spots. If you punch a hole in a balloon, it pops.
• The Fix: They made the holes with rounded edges (like a smooth archway) and reinforced them. They also placed the heavy vacuum pumps far away from the jar using long, flexible tubes so the pump's magnetic field doesn't interfere with the plasma.

Summary: Why Does This Matter?

This paper is essentially a blueprint and a safety report for a new, compact fusion machine.

The engineers proved that:

1. The design is structurally sound (it won't crumble).
2. The design is thermally sound (it won't crack when baked).
3. The design is smart (using electrical breaks and double seals to keep the plasma happy).

By building this "fat donut" machine, India's private sector is taking a big step toward the future of clean, limitless energy. It's like building a prototype for a car engine before you try to win the Formula 1 race.

Technical Summary

Here is a detailed technical summary of the paper "Design and mechanical analysis of the PRAGYA tokamak vacuum vessel."

1. Problem Statement and Context

The paper addresses the design and structural validation of the vacuum vessel (VV) for PRAGYA, India's first privately developed low-aspect-ratio tokamak, designed by Pranos Fusion Energy.

• Device Specifications: The tokamak targets a plasma major radius ($R_0$) of 0.4 m, minor radius ($a$) of 0.13–0.18 m (Aspect Ratio $A \approx 2.2$), plasma current ($I_p$) up to 25 kA, and a toroidal magnetic field ($B_T$) of 0.1 T.
• Engineering Challenges: The vacuum vessel must maintain a high vacuum ($10^{-6}$ mbar) while withstanding complex multi-physics loads:
  • Atmospheric Pressure: The differential pressure between the vacuum interior and the atmosphere.
  • Self-Weight: Gravity acting on the vessel and its support structure.
  • Thermal Loads: Stress induced during the "baking" process (heating to 150°C) to remove adsorbed gases.
  • Electromagnetic Loads: Induced eddy currents during plasma current ramp-up/down and potential disruption events.
  • Geometric Constraints: The need for multiple diagnostic ports, fuel injection, and pumping systems without compromising structural integrity.

2. Methodology

The authors employed a comprehensive design and simulation workflow:

• Design Optimization:
  • Geometry: A toroidal vessel with a 6 mm wall thickness (SS304L) was selected after an optimization study to minimize stress while managing material costs.
  • Electrical Break: The vessel is split into two sub-tori separated by G10 (glass-reinforced epoxy) insulation to break the toroidal electrical path, minimizing eddy currents that could destabilize the plasma.
  • Sealing: A double O-ring arrangement with an evacuated interstitial space is used at the junction of the two sub-tori to ensure leak-tightness.
  • Stiffening: Internal ribs (stiffeners) with a $20 \times 20$ mm cross-section were added to the inner faces to increase rigidity and provide mounting points for limiters/diagnostics.
• Numerical Simulation (FEA):
  • Software: COMSOL Multiphysics 6.3 was used for 3D Finite Element Analysis (FEA).
  • Mesh Refinement: A grid convergence study was performed, utilizing a mesh of approximately 1.012 million elements to ensure accuracy, particularly around stress concentrators like ports and stiffeners.
  • Load Cases: Simulations were run for:
    1. Vacuum + Self-weight.
    2. Baking (150°C) + Vacuum + Self-weight.
    3. Linear Buckling analysis for support legs and the full assembly.
• Material Properties: Stainless Steel 304L (SS304L) was chosen for its non-magnetic properties, corrosion resistance, and mechanical strength. Properties were adjusted for room temperature (20°C) and baking temperature (150°C).

3. Key Contributions

• First Private Indian Tokamak Design: Detailed the mechanical design of the first low-aspect-ratio tokamak developed by a private entity in India.
• Innovative Sealing and Insulation: Proposed and validated a double O-ring system with an evacuated gap for the electrical break junction, ensuring both vacuum integrity and electrical isolation.
• Stress Reduction via Stiffeners: Demonstrated through simulation that adding internal stiffeners reduces maximum von Mises stress by a factor of 6 to 7 compared to an unstiffened vessel.
• Comprehensive Thermo-Mechanical Analysis: Provided a coupled analysis of thermal expansion and mechanical stress during the baking cycle, a critical step often overlooked in preliminary designs.

4. Key Results

• Wall Thickness Optimization: A 6 mm wall thickness was determined to be optimal. A 4 mm wall resulted in ~200 MPa stress (near yield), while 6 mm reduced peak stress to 79 MPa under vacuum/self-weight alone.
• Vacuum & Self-Weight Load:
  • Max Stress: ~110 MPa (occurring at the top trapezoidal port interface and stiffener junctions).
  • Max Deformation: ~0.5 mm at the bottom plate.
  • Safety Margin: The stress is well below the yield strength of SS304L (170 MPa).
• Thermal Load (Baking at 150°C):
  • Max Stress: ~280 MPa at the inboard side and stiffener merges.
  • Safety Assessment: While 280 MPa exceeds the yield strength, the authors classify thermal stress as secondary stress. According to ASME criteria, the allowable limit for combined primary and secondary stress is $2 \times$ yield strength (340 MPa). Thus, the design is safe.
  • Deformation: Max thermal deformation was ~2.1 mm at the top of the vessel. The design includes expandable washers and oversized bolt holes to accommodate this expansion without inducing excessive stress.
• Buckling Analysis:
  • Support Legs: Critical Load Factor (CLF) > 100 (Safety Factor ~120).
  • Full Assembly: CLF > 44 for the lowest buckling mode (twisting), confirming stability against collapse under self-weight and pressure differential.

5. Significance

This paper establishes a robust engineering foundation for the PRAGYA tokamak, proving that a compact, low-aspect-ratio design can meet stringent structural and vacuum requirements.

• Validation of Design: The FEA results confirm that the vessel can safely operate under combined mechanical, thermal, and vacuum loads with significant safety margins.
• Enabling Future Research: By validating the structural integrity, the design enables subsequent phases of the project, including plasma operations, testing of superconducting magnets, and investigation of MHD stability.
• Scalability: The design principles (electrical breaks, double O-ring sealing, stiffener integration) offer a blueprint for future compact fusion devices, particularly for private sector fusion startups aiming for cost-effective, modular reactor designs.

The paper concludes that the PRAGYA vacuum vessel is structurally sound and ready for fabrication, with future work planned to analyze electromagnetic loads during plasma disruptions.