Chapter 297 Modeling Plasma Turbulence

After sending David McGumilan, the head of Princeton's chemistry department, away, Xu Chuan put his energy back into the control of ultra-high temperature plasma.

The essence of this job is actually to establish a mathematical model for turbulence. Of course, to be more practical, it can be said to be a study of the phenomenon of plasma turbulence.

In fact, in terms of difficulty, studying the phenomenon of plasma turbulence is not much easier than studying one of the seven millennium problems.

First of all, turbulence is a famous chaotic system, and it is also one of the problems that many physicists and mathematicians are at a loss, not to mention plasma turbulence in turbulence.

And what he wants to study is not only plasma turbulence, but also ultra-high temperature plasma turbulence in the chamber of a controllable nuclear fusion reactor, which is nearly two orders of magnitude higher than turbulence.

Although he has made great progress in the NS equation and has a theoretical foundation, it is still difficult to solve this problem.

Not to mention the study of turbulence and NS equations in mathematics, even if he is not the first person, he can rank in the top three.

The key lies in application. At present, most of the results achieved in the application of turbulence and plasma fluids are mixed with experimental experience and some experimental parameters.

For example, Princeton's PPPL plasma laboratory has its own phenomenological model, which was made by mathematicians and physicists in the Princeton Institute for Advanced Study for PPPL equipment.

This is also the reason why Princeton can provide help to other experimental institutions in the United States that study controlled nuclear fusion.

And it is very difficult to start from mathematical theory and set aside these experimental experience and experimental parameters to establish a comprehensive model.

At Nanjing University, Xu Chuan sat in his office, scribbling on the manuscript paper with a black ballpoint pen in his hand.

[μi(t)=1/T∫t+Tˇt0μi～(t)dt]

[μi(t)=LimT→∞1/T∫t+Tˇt0μi～(t)dt]

For a turbulent flow, the most commonly used method in the mathematical community is to use the statistical average method to open the turbulent research.

In the past, when mathematicians studied turbulence, they decomposed irregular flow fields into mean fields and non-pulsating fields, which also led to the century-old problem of blocking the Reynolds equation.

The random statistical average method of turbulence is the fundamental means of dealing with turbulent flow, which is determined by the randomness of turbulence.

What he is doing now is to start from the mean field and the non-pulsating field, try to explain the two in mathematical language, and make a connection.

Starting from this step, it may be possible to complete the model for plasma turbulence.

After all, no matter how complex turbulence is, its problem itself, from the perspective of physics, is mainly derived from two aspects: "external environmental interference" and "classical complexity itself".

External environmental interference is easy to understand, just like when a car is driving on a highway, its own shape, wind resistance and other factors will bring vortices to the rear of the car. Including if there are large trucks or other vehicles passing by during driving, a more complex turbulent system will be formed.

This is also the reason why top sports cars or racing cars pursue the ultimate appearance and ultimate fluid dynamics of the vehicle, because the existence of turbulence will increase wind resistance, consume more power and reduce speed.

Of course, this is also the manifestation of fluid mechanics applied to actual industry.

As for the classical complexity itself, this comes from classical physics.

In classical physics, there is a method called "reductionism", which is the content of high school in the nine-year compulsory education.

At that time, when we learned physics, we would tell you that Newton's law started from a particle, Coulomb's law started from a point charge, Biot-Savart's law started from an electric current element, and vibration fluctuations started from a simple harmonic oscillator.

From simple to complex, layer by layer, to achieve the purpose of understanding the material world.

Since Newton, people have firmly believed that everything, including the vast and infinite universe, can be calculated. This is the so-called computationalism + reductionism.

Computationalists believe that even human nature can be calculated, which even affects the development of artificial intelligence today.

And reductionism is to subdivide matter into basic units bit by bit, and then establish the evolution equation of motion based on the interaction law between basic components.

This sounds simple and easy to understand.

But how easy is it to reconstruct the evolution equation from basic components?

Just like a car driving on a highway, it is generating and annihilating eddies and turbulence every moment.

Especially at the rear of the car, the situation is even more serious. A car driving on the highway, the air flow brought by its own driving alone, contains at least 1000000000000 microflow units.

If there are other vehicles passing by, this number will increase by several orders of magnitude, at least reaching the level of one trillion.

To analyze the structure of so many microflow units, we must also consider the disturbances caused by these microflow units to each other, the medium and large microflow units merged, the dissipated microflow units, and the newly formed microflow units every moment.

Believe me, analyzing so many microflow units is definitely not something that any computer you can buy on the market can handle.

Even supercomputers cannot do real-time analysis because the amount of data is too large.

If you want to analyze and process these things, the only way is to establish a simulation, commonly known as CFD.

Its basic principle is to numerically solve the differential equations that control fluid flow, and obtain the discrete distribution of the flow field of fluid flow in a continuous area, so as to approximately simulate the fluid flow.

This technology has actually been widely used in all walks of life.

From movable cars, airplanes, rockets to immovable high-rise buildings, building ventilation, daily air conditioners, refrigerators, etc., all have traces of it.

However, most of the time, the results obtained by CFD simulation are very different.

Not to mention the simulations established by different CFD methods, even the simulations established by the same method for the same object, such as aircraft driving, have different results.

Just like the difference between domestic and foreign aircraft is not only in the engine, there is also a very obvious distance in the application of fluid dynamics.

This gap is mainly reflected in the reaction force and dynamic balance of the aircraft when responding to dangerous conditions.

For example, when encountering thunderstorms and storms, the aircraft can quickly adjust the balance of the fuselage through the computer.

Or it can be reflected in the pilot's control over the aircraft when the fighter is doing those extremely difficult actions. Don't underestimate the fluid and turbulence that pass through the surface of the fuselage, they still have a considerable impact on the balance of the aircraft.

And this is why the NS equation is pursued by countless mathematicians and physicists.

By solving it, each phased result can greatly improve human understanding of fluids in the future.

These things can be transformed into mathematical models or other things to help improve people's control and application of fluids.

As the research deepened, Xu Chuan began to devote himself to it.

Even the research address was moved back to the villa from the office of Nanjing University, and the students in the school who had just enjoyed his class for a few days were cut off again.

For the ultra-high temperature plasma in the chamber of the controllable nuclear fusion reactor, whether it is the current mainstream tokamak device, the stellarator, or the spherical NIF ignition device, the plasma inside is in a limited space.

Based on the interim results of the NS equation, he began to sort out the experimental data of PPPL that he brought back from Princeton bit by bit, and then substituted it into it to prepare for the establishment of a mathematical model.

This is a rather tedious task, but Xu Chuan found that this work did not seem as difficult as he imagined.

He had originally prepared to be stuck on this job for several months or even a year or two. But now, he was a little surprised to find that his progress seemed to be quite smooth so far.

Looking at the manuscript on the desk, Xu Chuan smiled: "It doesn't seem that difficult, maybe this problem can be solved soon!"

Full of motivation, he once again devoted himself to the research.

Days passed one by one, and I don't know how long it has passed.

In the study, Xu Chuan looked up at the previously sorted data on the computer screen, while waving the ballpoint pen in his hand to continue writing some mathematical formulas on the manuscript paper.

"(τ)/Vi(t)=1/▽i(ξ，η，ζ，t)dξdηdζ，ft+ξ·xf=1κQ(f， f),."

Staring at the data written on the manuscript, he frowned and fell into deep thought.

At this point, he has been able to describe the plasma flow in the reactor chamber through mathematical equations, but new problems have also emerged.

At present, he can only describe the turbulent flow field with a nearly uniform volume mean, while the relatively chaotic non-pulsating field is still a mystery.

After thinking for a while, Xu Chuan threw the ballpoint pen aside, leaned back on the chair, and stared at the ceiling silently.

After a while, he let out a long sigh and shook his head helplessly, saying to himself: "It seems that setting a flag before doing research is really not a good thing."

At the beginning, when he went deep into the core research, it was too smooth, so he thought that he could get results quickly with sufficient theoretical support, which made him confidently set a flag.

But now it seems that he still has no idea how far he is from the exit of this maze.

He even began to doubt that the path he was taking might be problematic.

As we all know, at the macroscopic scale, gases and fluids are regarded as a continuum.

Their motion is described by macroscopic quantities such as material density, macroscopic velocity, absolute temperature, pressure, tension, heat flow, etc.

But on the contrary, at the microscopic scale, gases, fluids and even any matter are regarded as a multi-body system composed of microscopic particles (atoms/molecules).

Among the equations proposed in fluid mechanics, the most famous are the (compressible or incompressible) Euler equations and the Navier-Stokes equations.

However, in the study of fluid dynamics, there is another famous equation, that is, the Boltzmann equation.

The Boltzmann equation is a partial differential equation that describes the statistical behavior of thermodynamic systems in non-thermodynamic equilibrium states, proposed by Ludwig Boltzmann in 1872.

It can be used to determine how physical quantities, such as heat and momentum, change during the transport of a fluid.

In addition, we can also derive other characteristic properties of fluids from it, such as viscosity, thermal conductivity, and electrical conductivity (considering the carriers in the material as gas).

But like the NS equation, the existence and uniqueness of the solution are still not completely solved.

However, when modeling plasma turbulence, Xu Chuan used part of the Boltzmann equation.

Although strictly speaking, the traditional Boltzmann equation is only applicable to neutral gas molecular systems, when it is applied to common non-equilibrium plasmas, including non-equilibrium plasmas flowing under atmospheric pressure conditions, the results are still correct after some corrections.

After all, theoretically, plasma can be regarded as a mixed gas composed of positive and negative charged particles.

Of course, this theory is not completely correct, and mathematically using the Boltzmann equation to study plasma requires some corrections, but it is not impossible to use it.

However, here, a new problem arises.

When using the Boltzmann equation to describe the turbulent flow field, a gully blocks the mean field and the non-pulsating field.

He couldn't find a suitable room to connect the two.

After staring at the ceiling for a while, Xu Chuan sat up straight again and picked up the ballpoint pen on the table.

No matter what, he would not give up.

Even if this was a road that no one had ever touched, and no one could provide him with experience and knowledge. He would not give up even if he had to conquer all the thorns and difficulties along the way.

Moreover, it was precisely because of the difficulties that people had the desire to conquer, and the satisfaction after solving the problem.

If there was no bridge connecting the average field and the non-pulsating field, then he would build a bridge over this abyss.

The purpose of his life of focusing on mathematics was not to go one step further on the original peak. Now the road was under his feet, so he just had to move forward.

At the desk, Xu Chuan held a pen and stared at the formula on the manuscript paper and thought.

"In theory, plasma contains multiple particles, at least ions and electrons, so it can be regarded as the Boltzmann equation under a multi-particle system.

"In controlled nuclear fusion, the plasma in the reactor is usually composed of 5% hydrogen ions and 95% deuterium ions. "

"If the distribution function of deuterium ion particles is fα(r,υ,t)drdυ, then the kinetic equation of evolution in phase space is: fα/t+V·fα/r+Fα/mα·fα/v=（fα/t）."

"If the distribution function of hydrogen ion is..."

Bit by bit, Xu Chuan sorted out what he needed from the source, and occasionally turned on the computer to search for some necessary information.

This is a very difficult task, and there are not many papers to refer to.

After all, no one has ever gone to this level in the model theory of plasma turbulence.

The days passed by day by day, and Xu Chuan didn't know how long he had been in the study. In order to build this microscopic bridge between the average field and the non-pulsating field, he spent almost all his time exploring feasible solutions except for eating and sleeping.

So much so that when Zheng Hai knocked on his door, he was startled.

"Professor, how did you get into this state? "

When Xu Chuan opened the door, Zheng Hai was shocked. Who was this man with messy hair, a beard that looked like he hadn't worn it for half a month, bloodshot eyes, and even dark circles?

If he hadn't confirmed that this was Xu Chuan's study, he would have thought that Xu Chuan had been replaced.

"What's the matter?" Xu Chuan asked, looking up. Although the fatigue on his face was obvious, his eyes were unusually bright.

These days of busyness were not without gain. Between the average field and the non-pulsating field, he had found a way to the other side.

"It's about the nuclear waste power generation project. The nuclear energy industrial park over there has passed the acceptance inspection. A celebration banquet and commendation meeting have been arranged. Let me inform you." Zheng Hai said quickly.

"Let them open it. I won't go. I don't have time recently. "

Xu Chuan replied without hesitation. The research on plasma turbulence has now reached a critical point. He did not want to interrupt his train of thought and go to Beijing to receive the award.

"Uh"

Zheng Hai was stunned for a moment, and said with a smile: "This is not good, after all, you are the general manager."

Although he is not a scientific researcher, he has been following Xu Chuan throughout the process, so he knows very well the contribution of this person in front of him to the project.

It can even be said that this celebration banquet and commendation meeting was held specifically for him.

If he doesn't go, the remaining researchers and engineers will probably be scared and dare not accept the commendation~