Synchrotron radiation leveling at future circular hadron colliders

This paper proposes and analyzes a novel "synchrotron radiation power leveling" strategy for the Future Circular Collider (FCC-hh), where beam energy is dynamically adjusted during a physics store to manage heat loads from synchrotron radiation, thereby increasing both peak and integrated luminosity and significantly boosting the production rates of key physics processes like di-Higgs events.

The Gist

Imagine you are running a massive, high-speed train station (the Future Circular Collider, or FCC-hh) where two streams of tiny particles (protons) crash into each other to create new physics. The goal is to get as many "crashes" (collisions) as possible to discover new particles, like the elusive "double Higgs boson."

However, there's a catch. As these trains speed up to near the speed of light, they start glowing with intense heat due to friction with the magnetic fields guiding them. This is called synchrotron radiation.

In the past (at the current Large Hadron Collider), this heat was negligible. But for the future 100-TeV collider, the heat is so intense that it threatens to melt the super-cooled magnets. To prevent this, the station has a strict heat limit. If the trains are too fast and too crowded, the cooling system can't keep up.

The Problem: The "Too Hot to Handle" Dilemma

Usually, you want your trains to be:

1. Fast (High Energy): To smash particles hard enough to create heavy new things.
2. Crowded (High Current): To have as many collisions as possible.

But the heat limit says: "You can't have both at the same time."

• If you run at maximum speed with a full train, the magnets overheat.
• If you slow down to cool the magnets, you lose the ability to create heavy particles.
• If you reduce the number of passengers (protons) to keep the heat down, you get fewer collisions.

The Solution: "Synchrotron Radiation Leveling"

The author, Frank Zimmermann, proposes a clever new strategy called Synchrotron Radiation Leveling. Think of it like driving a car up a steep mountain while trying to keep your engine temperature exactly at the limit without overheating.

Here is how the two main strategies work, using simple analogies:

Strategy 1: The "Two-Step" Hike (One-Step Leveling)

Imagine you are hiking up a mountain.

• Phase 1: You start at the bottom (Lower Energy, 12 Tesla magnets). You carry a heavy backpack (High number of protons). Because you are moving slower, the heat generated is manageable, even with the heavy load. You collect a lot of "scenic views" (collisions) here.
• The Switch: As you hike, your backpack gets lighter (protons burn off in collisions). Because you have less weight, you can now speed up!
• Phase 2: You switch to the steeper, faster path (Higher Energy, 14 Tesla magnets). Even though you are going faster, your backpack is now so light that the heat generated is still within the safety limit.

The Result: You get the best of both worlds. You collected data at the lower energy with a full crowd, and then you collected data at the higher energy with a lighter crowd, all without ever breaking the heat limit.

Strategy 2: The "Smooth Cruise" (Continuous Leveling)

Instead of switching paths abruptly, imagine you are on a treadmill that slowly speeds up.

• As the crowd of passengers naturally thins out (because they are getting off at the destination), the machine automatically and continuously increases the speed.
• The speed increases just enough to compensate for the fewer passengers, keeping the "heat output" perfectly constant at the maximum allowed limit.

The Result: You are constantly operating at the absolute edge of what the machine can handle, squeezing out every possible drop of performance.

Why Does This Matter? (The "Double Higgs" Bonus)

The paper highlights a specific goal: creating Double Higgs bosons.

• Making these particles is like trying to hit a bullseye with a dart. It's hard.
• The "bullseye" gets slightly bigger as you go faster (higher energy), but not by much.
• However, the number of darts you can throw (luminosity) drops drastically if you are forced to slow down to cool the machine.

By using this "Leveling" strategy:

1. You keep the machine running at full capacity (maximum heat) for longer.
2. You get to use the higher speeds for a significant portion of the run.
3. The Payoff: The paper calculates that this method could increase the number of Double Higgs events by 60% to 120% compared to the old way of just running at a fixed speed.

The Catch: The "Recipe Book" Problem

There is a small hurdle for the scientists analyzing the data.

• Old Way: The experiment runs at one speed. The computer programs (simulations) know exactly what to expect.
• New Way: The speed is constantly changing. It's like a chef cooking a meal where the oven temperature is slowly rising the whole time. The computer programs need to be updated to understand that the "recipe" (physics rules) changes slightly with every degree of speed.

The author suggests that a "Two-Step" approach (switching speeds once or twice) is the sweet spot. It gives you most of the performance boost but is much easier for the computers and detectors to handle than a constantly changing speed.

Summary

The paper proposes a smart way to run the world's most powerful future particle collider. Instead of running at a fixed speed and risking overheating, we should slow down when the crowd is heavy, and speed up as the crowd thins out. This keeps the machine at its maximum safe limit the entire time, allowing us to discover new physics much faster than previously thought possible.

Technical Summary

Here is a detailed technical summary of the paper "Synchrotron radiation leveling at future circular hadron colliders" by F. Zimmermann.

1. Problem Statement

The High-Luminosity LHC (HL-LHC) utilizes luminosity leveling (adjusting crossing angles or $\beta^*$) to manage event pile-up. However, for the proposed Future Circular hadron Collider (FCC-hh), operating at center-of-mass energies of 70–90 TeV, a new physical constraint emerges: synchrotron radiation (SR).

• Heat Load Limitation: At these energies, SR emitted inside the cold superconducting magnets creates a significant heat load. This load is limited by the capacity of the cryogenic systems, effectively capping the total allowable beam current.
• Emittance Damping: Unlike the LHC, where intrabeam scattering dominates, the FCC-hh will experience rapid transverse and longitudinal emittance damping due to strong SR (damping times of 1–2 hours).
• The Conflict: Operating at maximum design energy (e.g., 14 T dipole field) with high initial beam currents would exceed the SR heat load limit. Conversely, operating at lower currents to satisfy the heat limit reduces peak luminosity. Furthermore, the rapid emittance damping causes the beam-beam tune shift to increase during a physics store, potentially hitting the beam-beam limit before the beam is fully consumed.

The core problem is how to maximize the integrated luminosity and physics output (specifically rare processes like di-Higgs production) while respecting the SR power limit and managing the dynamic evolution of beam parameters.

2. Methodology

The author proposes a novel operational mode called Synchrotron Radiation Power Leveling. Instead of running at a fixed beam energy, the beam energy is adjusted (increased) during a physics store as the beam current decreases due to proton burn-off.

The paper develops analytical models for three scenarios:

1. Fixed Energy: Conventional operation at a single energy (12 T or 14 T).
2. One-Step Leveling: The collider starts at a lower energy (12 T) with high intensity. Once the beam current drops sufficiently to allow an energy increase without exceeding the SR power limit, the dipole field is ramped up to the maximum (14 T).
3. Continuous Leveling: The beam energy is continuously adjusted throughout the store to maintain a constant SR power level. This involves a continuous increase in energy as the bunch population ($N_b$) decreases, governed by the relation $E \propto N_b^{-1/4}$.

Key Mathematical Framework:

• SR Power Constraint: $P_{SR} \propto N_b E^4$. To keep $P_{SR}$ constant, as $N_b$ drops, $E$ must rise.
• Beam Dynamics: The model couples the evolution of bunch intensity ($N_b$), emittance ($\varepsilon$), and luminosity ($L$).
  • Emittance decays exponentially due to radiation damping ($\varepsilon \propto e^{-t/\tau}$).
  • Intensity decay is driven by burn-off ($dN_b/dt \propto -L$).
  • The beam-beam tune shift ($\Delta Q$) is monitored to ensure it does not exceed the maximum acceptable limit ($\Delta Q_{max}$).
• Optimization: The authors derive equations to find the optimum run time ($t_{r,opt}$) that maximizes the average luminosity, accounting for the "turnaround time" (time required to refill the machine).

3. Key Contributions

• New Operational Paradigm: Introduction of SR power leveling as a necessary strategy for 100 TeV-class colliders to overcome cryogenic heat load limits.
• Analytical Solutions: Derivation of closed-form analytical expressions for the time evolution of beam intensity, emittance, and luminosity under both step-wise and continuous energy leveling.
• Performance Modeling: Detailed simulation of the FCC-hh performance for two dipole field scenarios (12 T and 14 T), comparing fixed energy, one-step, and continuous leveling.
• Physics Impact Assessment: Quantification of the gain in rare physics processes, specifically di-Higgs production, which benefits significantly from the increased integrated luminosity at lower energies where the cross-section is still substantial.

4. Results

The study compares the performance of the FCC-hh under different leveling schemes (assuming 160 days of operation/year and 70% machine availability).

Luminosity Performance:

• Fixed Energy (14 T): Yields a total integrated luminosity of 0.7 ab$^{-1}$/year per interaction point.
• Fixed Energy (12 T): Yields 1.3 ab$^{-1}$/year.
• One-Step Leveling (12 T $\to$ 14 T): Achieves 1.3 ab$^{-1}$/year total, but crucially, delivers 0.6 ab$^{-1}$ at the high energy (14 T) and 0.7 ab$^{-1}$ at the lower energy. This is a significant improvement over running exclusively at 14 T.
• Continuous Leveling: Achieves 1.7 ab$^{-1}$/year total. It delivers 1.0 ab$^{-1}$ at intermediate energies (72–84 TeV) and 0.7 ab$^{-1}$ at the maximum 14 T.

Physics Gain (Di-Higgs Production):

• The di-Higgs cross-section is energy-dependent but remains high at lower energies.
• One-Step Leveling: Increases di-Higgs event yield by ~64% compared to fixed 14 T operation.
• Continuous Leveling: Increases di-Higgs event yield by ~120% (more than double) compared to fixed 14 T operation.
• Compared to fixed 12 T operation, continuous leveling still offers a ~35% gain in di-Higgs events.

Operational Parameters:

• Turnaround Time: The optimal run times are approximately 4.4–5.8 hours depending on the scenario.
• Bunch Intensity: Continuous leveling allows for higher initial beam currents because the energy is ramped up only as the current drops, keeping the SR power within limits.

5. Significance and Implications

• Maximizing Physics Reach: This mode of operation allows the FCC-hh to explore a wider range of collision energies within a single fill, significantly boosting the statistics for processes that are not solely dependent on the highest possible energy (like di-Higgs production).
• Detector Challenges:
  • Step-wise Leveling: Considered feasible. Experiments can split data into distinct datasets corresponding to different energy steps. Trigger menus can be adjusted via "keys" for each step.
  • Continuous Leveling: Poses significant challenges for data analysis and Monte Carlo (MC) simulations. Current MC generators cannot handle continuously varying center-of-mass energies. This would require new software to re-weight samples based on energy and pile-up, and interpolation algorithms for cross-sections and Parton Distribution Functions (PDFs).
• Strategic Recommendation: The author suggests that while continuous leveling offers the highest physics gain, a multi-step (staircase) leveling scheme (e.g., 3–4 discrete steps) might be the optimal compromise. It would capture most of the physics benefits of continuous leveling while remaining manageable for detector simulations and data analysis.

Conclusion:
Synchrotron radiation power leveling is a critical operational strategy for the FCC-hh. By dynamically adjusting beam energy to match the decreasing beam current, the collider can operate at the maximum allowable SR power limit throughout the fill. This approach significantly increases the integrated luminosity and, more importantly, the yield of rare physics events, justifying the development of new operational modes and detector analysis frameworks.