Controlling Optical Phase Drift for Better Laser-Plasma Accelerators

A novel method for controlling combined-beam laser pulses could pave the way for smaller, more capable particle accelerators and colliders.

By Carl A. Williams, February 23, 2023

Since their invention in the 1930s, particle accelerators have revolutionized science. They have allowed scientists to study the origins of the universe and explore the subatomic world, leading to a deeper understanding of the building blocks of matter, the discovery of new elements, and advances in medical research and therapeutic treatments.

Recent advances in artificial intelligence and machine learning promise significant enhancements for particle accelerator operations, including applications in diagnostics, controls, and modeling. They could also help to usher in next-generation plasma-based accelerators that are more compact, capable, and cheaper to build and operate than current devices; fusion reactors that harness the same processes that power the sun, providing unlimited, carbon-free energy; and greatly improve the performance of technologies that employ complex control systems.

Machine learning and beam combining

Combining the beams from many low-powered fiber lasers to make high-powered, ultra-fast beams is a promising technology for powering next-generation laser-plasma particle accelerators (LPAs). Researchers from the Accelerator Technology & Applied Physics (ATAP) Division, in collaboration with the Engineering Division and Computational Research Division, have found a way to make laser pulse combining more efficient by correcting for optical phase shifts, resulting in a powerful coherent beam. It could be an enabling technology for new types of lasers and for the precision control of accelerators and complex systems that extend the performance of future accelerators and other technologies, including fusion reactors. 

The multidisciplinary team calls their approach the “deterministic differential remapping method,” or DDRM. It uses a neural network to correct for optical phase shifts in the input beams of a coherent beam-combined (CBC) laser to generate ultra-fast laser pulses with sufficient power to drive an LPA.

LPAs work by using intense laser bursts passing through a plasma to create a moving wave capable of accelerating charged particles at rates of up to a thousand times greater than conventional approaches. This capability could usher in a new era of particle accelerators that are more compact and much less expensive than current technologies.

“Developing the DDRM was very exciting for us,” says Dan Wang, Research Scientist in ATAP’s Accelerator Controls & Instrumentation (BACI) Program, “as this is the first time that machine learning has successfully been shown to control the stability of the diffractive combining that is a key element of these lasers. Our work also demonstrates how machine learning can be inspired by physics, guided by physics, and benefits physics.”

The DDRM, explains Wang, operates similarly to how a human would learn to control a CBC laser if they had no phase information for the input beams by “adjusting the system’s control knobs and checking to see how those adjustments affect the output beam.”

While CBC lasers show great promise for delivering the high-power pulses needed for LPAs, it has proved very challenging to maintain the coherence and stability of pulses that are required to operate at frequencies in the 1-100 kHz range—a repetition rate necessary to realize the full potential of LPAs.

For instance, mechanical and thermal perturbations from the environment, such as table movements or variations in air flow or temperature can cause the optical phases of the individual input beams to drift, which introduces instabilities into the combined beam. The effects of which are compounded by power fluctuations in the input beams, laser pointing errors, and polarization instabilities.

“The profile and alignment of the input beams also determine the stability of the combined beam,” says Qiang Du, a Staff Scientist from the Engineering Division who is also part of ATAP’s BACI Program, and who is working with Wang, Russell Wilcox, and Tong Zhou in the team that developed the DDRM. “So, if you multiply the factors that determine beam stability with the number of input beams, you will easily have hundreds of knobs to control.”

Some of these parameters, he continues, also tend to change spontaneously, making controlling optical phase drift increasingly challenging.

He says maintaining the correct phasing of the input beams and maximizing the combination efficiency is essential for generating high-power laser pulses from input beams with limited output.

Although there are several methods commonly used for controlling beam stability—including reference beams, phase retrieval, and Stochastic Parallel Gradient Descent (SPGD)—these techniques either introduce further complexity into the optical systems of a CBC laser or would be too slow in cases where hundreds of lasers are combined at greater than kilohertz repetition rates.

For example, SPGD uses “guess” or search algorithms and requires hundreds of convergence steps to correct for optical phase drift. And these methods are not scalable, making them too slow to produce a CBC laser pulse with sufficient power to accelerate particles to the energies required in LPAs.

“It is almost too hard to control the beam deterministically, which is why ‘dither and search’ SPGD is often used to correct phase drifting because it is easy,” says Du. “However, it is slow and introduces noise into the system.”

“We are talking about nanometer levels of control precision, so we need to be able to control the beams to within a couple of degrees of optical phase while they operate at frequencies up to hundreds of terahertz.” 

He notes this is highly challenging, especially with large beam arrays and when things are changing fast, as errors need to be rapidly recognized and corrected. “That is why we say the challenge is ‘almost too hard.’”

Given these challenges and the limitations of current beam control methods, the team turned to Machine Learning Control. This approach uses data-driven machined learning, along with methods developed from control theory, to train neural networks to solve optimal control problems for complex systems like those encountered in CBC laser systems. 

A new approach pays off

In 2021, simulations by the team demonstrated that a machine-learning-based algorithm could successfully control an 81-beam combiner operating on an experimentally calibrated numerical model.

“Although this required calibration of the optical system, the simulation showed that a neural network could detect phase errors based on interference pattern recognition of uncombined beams next to the combined beam,” says Wang. Moreover, she continues, the technique was up to ten times faster than SPGD using a single-detector and random dither. 

“However,” she added, “because most CBC lasers rely on uncontrolled parameters that slowly drift, a neural network trained to control the CBC laser system using one set of parameters may not be able to control the system should those parameters change.”

Initial training of the neural network can be problematic, too, notes Wang. “For instance, if the system is initially unstable, the input and output values will always be unknown due to phase errors, causing them to drift over time.”

To overcome this, the DDRM uses pairs of measurements separated by a predetermined step-change in the input phase to train the neural network. The process is fast enough that any phase drifting in the input beam array is rapidly adjusted to produce a coherent, stable output beam.

“And because the DDRM controls the CBC laser system deterministically, it is both fast and accurate, and can also be scaled up,” says Du.

By conducting simulations on various combined-beam arrays, the team demonstrated that the DDRM could be applied successfully to different types of coherent combining control, including temporal and spatial combining, where there are many outputs.

Du says they are now aiming to demonstrate that the method can be extended up to bandwidths of hundreds of kilohertz and in real time to ensure that there is no indeterministic latency that could introduce instability into the control system.

“We are also looking to demonstrate temporal pattern recognition control for the first time experimentally,” he says. “It will be the DDRMs’ ability to perform complex temporal stacking control and spatial combining control, which are critical to power-scaling for high-power lasers, that could make it a promising technique for producing lasers with the power to drive LPAs.”

Potential that extends beyond lasers

While the work has led to machine learning models that learn from laser patterns, Wang says that the DDRM could also see use in other systems that require fast and intelligent controls.

“These models could also be trained to learn from other types of patterns, such as those generated by electron beam or radio frequency signals in conventional accelerators, or patterns in quantum information processors.”

Wang is now working with Tengming Shen at ATAP’s Superconducting Magnet Program to develop machine learning-based pattern recognition for quench protection in high-temperature superconducting magnets. Quenches, or transitions from superconductivity to normal conductivity in part of a magnet, cause interruptions to operations and can damage equipment. This work, Wang notes, “is already showing promising results from simulations.”

“We are also applying machine learning controls to field-programmable gate arrays for faster inference of the control loop, which could enable kilohertz-level controls and lead to better control performance in the future,” she added. 

Commenting on the research, ATAP Division Director Cameron Geddes said: “This is an outstanding example of how Berkeley Lab team science, with multiple disciplines and parts of the organization collaborating, creates new methods. Here, not only do they enable new types of lasers, but also control methods with broad importance to extend the performance of future accelerators and related complex systems.”

In addition to the published papers, the research underpinning the development of the DDRM was also presented at the 20^th Advanced Accelerator Concepts Workshop, held from November 6-11, 2022, in Long Island, New York.

 

To learn more …

1. Wang, D., Du, Q., Zhou, T., Gilardi, A., Kiran, M., Mohammed, B., Li, D., and Wilcox, R., “Machine Learning Pattern Recognition Algorithm With Applications to Coherent Laser Combination,” IEEE Journal of Quantum Electronics, Vol. 58 (6), 2022, https://doi.org/10.1109/JQE.2022.3204437
2. Du, Q., Wang, D., Zhou, T., Gilardi, A., Kiran, M., Mohammed, B., Li, D., and Wilcox, R. “Experimental beam combining stabilization using machine learning trained while phases drift”, Optics Express 30 (8), 2022, https://doi.org/10.1364/OE.450255
3. Wang, D., Du, Q., Zhou, T., Li, Derun, and Wilcox, R., “Stabilization of the 81-channel coherent beam combination using machine learning,” Optics Express 29 (4), 2021, https://doi.org/10.1364/OE.414985

Written by Carl A. Williams or other authors as credited.

For more information on ATAP News articles, contact Carl A. Williams (caw@lbl.gov).