Into Unscientific

"????"

Secret room.

Hearing what Hua Yun said.

On Lu Guangda's fair and round face known as "Doctor Doll", a bewildered expression suddenly appeared:

o.O?

What?

Is the neutron transport equation nonlinear?

How can this be?

To know.

The essence of the neutron transport equation is the derivation of moderation + diffusion.

The moderation process can be described in terms of energy reduction.

The process of diffusion introduces flux density—both concepts have been mentioned before.

The diffusion process is the free diffusion of large-scale thermal neutrons in the reactor to participate in the fission reaction and maintain the operation of the nuclear reactor.

This is the core and most critical of nuclear fission, and it is also a relatively complex research object.

But at the end of the day.

The so-called diffusion process still belongs to the evolution of neutron distribution along with the nuclear reaction.

at the same time.

The concept of neutron flux density has been defined above, that is, current density.

The change in neutron density apparently falls into three parts:

First, the source generates neutrons.

Second, neutrons are absorbed and consumed for fission.

Eventually, neutrons leak out of the system.

Here, the source can be denoted as S(r, t), and the leakage can be represented as J(r, t) by a divergence, where J(r, t) is the current density of neutrons leaving the system.

The nuclear reaction rate is as above R=Σa.

If the neutron density is represented by n, a continuity equation appears:

n(r,t)t=S(r,t)Σa(r,t)J(r,t)

At the same time, the flow of neutrons into and out of the system is driven by distribution, which is determined by the gradient.

J(r,t)=D(r,t).

Among them, D=λs/3 is a coefficient, called the diffusion coefficient.

It is not difficult to see from here.

The neutron transport equation is clearly a linear partial differential equation. Wait!

Think here.

Lu Guangda suddenly realized something, and suddenly looked at Hua Yun, the leader of the second group:

"Old Hua, you mean the neutron transport equation, in fact, there is a situation similar to the nonlinear Schrödinger equation?"

Hua Yun nodded vigorously:

"That's right."

Speaking of Schrödinger's name, everyone must be familiar with it - the descendant of Xue Rengui in the marketing slogan, a well-known cat abuser.

Among the many deeds of this boss, the Schrödinger equation is obviously a key point.

It is a basic equation in quantum mechanics proposed by Schrödinger himself, and also a basic assumption of quantum mechanics.

In Xu Yun's future generations.

Many consider it the most important equation in modern physics, if not one of them.

At the same time.

It is also a very complex linear partial differential equation.

For any atom—as long as the force field experienced by electrons can be represented by a centered force field, its Schrödinger equation can separate variables.

So in almost all situations.

The Schrödinger equation is a standard linear equation.

But there is a very special case.

That is, when the potential field depends on the wave function, the derived Schrödinger equation is nonlinear.

This situation generally occurs in plasma or optics in the application field, which is an extremely rare situation.

And right now, according to what Hua Yun said.

It seems that if the neutron transport equation changes in a particular region.

Is it really possible?

Think here.

Lu Guangda picked up the document Hua Yun had brought over and read it carefully.

At the top of the file is a report on the capillary Petrov reactor, which is one of the only dozen or so non-cold burst nuclear reactor core data in the hands of the rabbits.

However, this report was not sent back to the country by the rabbits through special channels, but a reward given by Mao Xiong:

three years ago.

When Wang Ganchang was a researcher at the Maoxiong Dubna Joint Institute for Nuclear Research, he found a case of anti-sigma negative hyperons from 40,000 pairs of negatives. particle.

Negative hyperons belonged to one of the key areas that both Mao Xiong and Duan Hai were competing for. Wang Ganchang's discovery gave Mao Xiong a very useful chess piece in the field of theoretical physics.

Therefore, Mao Xiong presented this picture to Mr. Wang Ganchang as a reward.

Of course.

According to some situations declassified by later generations, this reward should be a choice made by the rabbits after internal discussions.

In addition, Mao Xiong also gave Mr. Wang Ganchang an invitation:

As long as he changes his nationality, he can stay in Moscow forever.

However, Mr. Wang finally rejected the invitation and returned to the motherland without hesitation. (This is something I only found out when I checked the information of this report, so I didn’t write it when I introduced Mr. Wang. In that era, you can see the shadows of these seniors in everything.)

alright.

The line of sight returns to reality again.

However, the data carrier on this document is not the black and white image that many people think, but a special tool in the early days of the scientific community:

paper tape.

In the 1960s and 1970s, watching paper tapes was considered a magical skill. There were a large number of top masters both at home and abroad, but it is a pity that it has almost been lost.

In the process of looking at the paper tape, scientists will brainstorm the images of the numerical simulation to analyze the calculation data recorded on the paper tape.

For example, the Manhattan Project.

Seaberg and Lawrence are experts in reading tapes and played a key role in the development of the atomic bomb across the sea.

Then Lu Guangda carefully picked up the roll of paper and looked at it seriously:

"Collision record number 45242, the fission secondary neutrons are approximated by isotropy."

"The dominant energy range of high-order neutrons is from 0.12 to 0.16, and the energy level of single-energy strong neutron sources is 14MeV"

"V1 is 2738 centimeters per microsecond, and the upper energy area is 42MeV"

The results looked at it.

Lu Guangda suddenly shrank his pupils:

"Eh? This is."

Only at this moment.

A set of numbers was impressively recorded on a piece of paper tape:

8.27^14g/cm.

And the parameters of this set of numbers are clearly written

The neutron density inside the device!

After that, Lu Guangda stared at the numbers, without saying a word.

well known.

The reason why the neutron transport equation can be regarded as a linear equation is that the neutron density in the system is usually much smaller than the atomic nucleus density—here, the small refers to the difference in magnitude, which is the so-called [much smaller than 】Degree.

For example, the earth and watermelons, or people and ants.

This is one of the basic physical assumptions made when deriving the neutron transport equation, and it is the foundation of all subsequent inferences.

Under this assumption.

We can only consider the collisions between neutrons and medium nuclei, but ignore the collisions between neutrons, and finally get a linear neutron transport equation.

But if the neutron density is so high that it is close to the atomic nucleus density or when the two are equivalent.

This assumption naturally fails.

And generally.

The density of atomic nuclei is usually of the order of .

10.14^14g/cm!

Although this number is not exactly the same as the neutron density on the paper tape, there is no difference in magnitude between the two:

For example, two people, A and B, A has 1 million assets, and B has 800,000 assets.

You can say that A is richer than B, but the gap between the two is not that big, maybe B will catch up with A within a few months.

In other words.

In this situation.

The neutron transport equation can no longer be regarded as a linear equation.

Then Lu Guangda looked at several other sets of data.

Finally, it is found that the neutron density will indeed increase dramatically in some special cases, approaching or even reaching the level of the atomic nucleus density.

These data include a large number of institutions in the three countries of China and the United States, and it is impossible for occasional errors to occur.

That is to say

The theory devised by Norris Bradbury was indeed wrong.

See this situation.

Lu Guangda's mood suddenly became a little dazed.

He wasn't lamenting that the project team spent a lot of time on the wrong path, but rather surprised.

The plan designed across the sea can go wrong?

But soon.

Another question popped up in Lu Guangda's mind:

The authority on the other side of the sea is also a human being. Why can’t mistakes be made if all technologies have not been implemented?

Don't say anything else.

If they are so invincible that everything is correct, they will be beaten so badly by us on the peninsula?

There are also Wang Ganchang and Zhao Zhongyao in the base, as well as Lao Yang and Lu Guangda who are still on the other side of the sea. Haven’t they also corrected a lot of wrong theories on the other side of the sea in the past? ——It’s just that the height is not as amazing as nuclear weapons.

Think here.

Lu Guangda couldn't help but took a deep breath, and his gaze was no longer misty, but was gradually replaced by a firm look.

Then he pondered for a moment, looked up at Hua Yun, and said:

"Old Hua, you have worked hard this time. Obviously, your verification is correct."

"Here I want to apologize to you and Comrade Ruiping. Because we didn't find the problem in the model, the comrades in the second and third groups were accused and pressured for no reason."

"As the person in charge of the project team, this is my dereliction of duty. I will actively review this matter at the next summary meeting."

Say it.

Lu Guangda turned to Xu Yun who was at the side again, and the expression on his face softened a lot:

"Comrade Han Li, I also want to express my gratitude to you—not only thank you for finding out the problem, but more importantly, let me understand a truth."

"That is, although the atomic bomb technology has been realized across the sea, it is still far from fully understood. There are still many mistakes and omissions that even an authority like Norris Bradbury cannot discover."

"This is undoubtedly good news. It means that although we are temporarily behind, we have not been pulled so far that it is difficult to catch up!"

"Maybe one day. Maybe we can surpass them."

When Lu Guangda spoke, he waved his right hand a few times in the air, appearing extremely powerful.

I heard this.

Xu Yun waved his hands quickly, and shook his head quickly:

"Director Lu, you are too serious. I just did some trivial work, and I really dare not take credit for it."

"If everyone is as polite as you and always raises trivial matters to the level of the state, then my consultant will not dare to speak up easily in the future."

Some of Xu Yun's remarks were out of politeness, and more of them were his real thoughts.

after all

The concept of the nonlinear neutron transport equation is the result of the 596 project team.

According to the information declassified by later generations.

throughout the development of nuclear weapons.

The rabbits found a total of 11 errors across the sea and Mao Xiong, among which there are two most important errors that can shake the cornerstone of nuclear engineering.

The first is the error discovered by Mr. Zhou Guangzhao about the energy distribution and angle distribution of secondary neutrons.

mentioned earlier.

At that time, in the early days of atomic bomb research, Mao Xiong experts provided some technical data related to atomic bombs.

However, when researchers used "nine calculations", which is a simulation method for solving equations, they found that the indicators of secondary neutron energy distribution and angular distribution did not match those provided by Mao Xiong.

In the end, Mr. Zhou Guangzhao started from the energy utilization rate, and used the "maximum work principle" to prove the correctness of the results of the "nine calculations" and the impossibility of the Maoxiong data.

Later, it can be seen from the documents decrypted by Mao Xiong.

This mistake was really not intentional, but a major mistake made by Sakharov, the number one nuclear weapon across the sea.

Except for Mr. Zhou Guangzhao.

The second major mistake the rabbits corrected was the nonlinear neutron transport equation.

This mistake was corrected relatively later, and the discoverer was Academician Du Xiangwan, who is still alive today.

Academician Du Xiangwan has won one special prize, one first prize and two second prizes of the National Science and Technology Progress Award, and more than ten provincial first and second prizes.

At that time, the rabbits had already begun to study the nuclear fusion of the hydrogen bomb.

As a result, Academician Du Xiangwan's team found that in actual engineering, in some places where the fusion reaction is very violent, the neutron density may be higher than the nuclear density.

This situation was later extended to the field of nuclear fission, that is, the atomic bomb, which brought a comprehensive innovation to the field of neutron transportation for nuclear weapons.

That's right.

This was during the development of the hydrogen bomb - when the bunnies had already detonated their first atomic bomb.

The rabbits on the atomic bomb used another approximate perturbation method, which did not involve the nonlinear neutron transport equation.

how to say

From the perspective of posterity.

A little better than the original linear neutron transport equation, but really limited.

If the linear neutron transport equation is a small electric donkey that can drive 10 kilometers, then the approximate perturbation method used by the atomic bomb can run 15 kilometers at most.

As for the conditions for the adaptation of the nonlinear neutron transport equation, it is.

One hundred thousand kilometers! ——This is the reason why there are no higher-level nuclear weapons today.

Wait until the 80s.

In order to be able to have a place in IUPAP, which is the highest organization in the international physics community, the International Union of Pure and Applied Physics.

The rabbits reluctantly published this technology on "Computational Physics", doi is 10.19596/j.cnki.1001-246x.1984.02.010.

This technology bought the rabbits the seat of IUPAP vice president, which was held by Mr. Zhou Guangzhao.

By the way.

This seat is not a vanity project, but a very important node in the history of rabbit modern physics.

for example.

Later, more than 90% of the first batch of non-Batumi instruments imported by domestic universities followed the IUPAP route.

As for that paper, which was still being cited even until 2018, it can be said to be an article with extremely far-reaching influence in the domestic physics community.

It is said. Just said.

It is said that today's hydrogen bomb technology across the sea also adopted this idea later - after all, before controllable nuclear fusion, nuclear fusion thermonuclear weapons must not escape the neutron transport equation.

And because of this.

Xu Yun still only played the role of a porter this time. It must be a bit of hard work, after all, his scars were exposed.

But if you want to say how much credit he has made, then he really can't afford it.

Indeed.

As a time traveler, it is impossible not to be a porter or a document copyer, and no one can avoid this.

But after carrying it, it is still a different matter to accept it calmly, claiming to be "pretending to be forceful and slapping face". (I saw a comment on a pirated book review website yesterday, saying that the protagonist is too cowardly, even if the other party is Yu Min or Qian Wushi, the protagonist should pretend to be aggressive, it is really weird)

all in all.

At this point, the remaining problems are very simple.

I saw Lu Guangda looked around, and then said:

"Okay, comrades, now that we have identified the problem, we should solve it next."

Say it.

Lu Guangda walked to the small blackboard, picked up the chalk and began to write:

"There are many ways to solve nonlinear equations, but the most commonly used method is the perturbation method, which is to convert nonlinear equations into a linear equation system."

"In the neutron transport equation, I think the nonlinear neutron transport equation can be transformed into a coupled linear equation system for solution."

"That is to say, the ones with no neutron collision, the one with one collision, and the one with two collisions... can get all the neutrons."

I heard this.

Everyone at the scene nodded their heads.

perturbation method.

This is indeed a fundamental method for nonlinear equations.

When Xu Yun mentioned to Qian Bingqiong that the world is nonlinear, he also mentioned this method.

introduced earlier.

There are two types of reactions between neutrons and nuclei:

Scattering and Absorption.

Among them, scattering is a kind of generalized scattering, that is, neutrons entering and exiting the nucleus remain unchanged, referred to as mid-exit.

This can be divided into two situations:

①Neutrons do not enter the nucleus.

That is to say, neutrons directly scatter with the nucleus, and in layman’s terms, they bounce off.

This is obviously an elastic scattering, energy and momentum are conserved, this kind of scattering is also called potential scattering.

②Neutrons are absorbed by the nucleus, but released again.

This situation is a little more complicated.

When the energy of the neutron is exactly the energy required by the nucleus to reach an excited state, the neutron is extremely easy to absorb:

Knowledge of energy level transitions from quantum mechanics can explain why this is so, a process called resonant absorption.

The recombination nuclei formed then emit neutrons and are classified as elastic/inelastic scattering according to whether energy is released.

The expressions for the two cases are as follows:

Non-elastic ZAX+ 01n[ ZA+1X] ZAX+ 01n

Elastic ZAX+ 01n[ ZA+1X] ZAX+ 01n+γ.

That's right!

Smart students must have seen it at a glance.

Resonance absorption requires neutron energy, so it has the characteristics of threshold energy.

In this way, the reaction of neutrons entering and neutrons exiting is the (n, n) reaction.

As for absorption, it is better understood.

To put it bluntly, neutrons go out of the nucleus.

There are three types of responses to this behavior:

One, radiation capture (n, γ).

The neutrons are absorbed by the nucleus, which regains a relatively stable state by emitting excess energy in the form of gamma rays.

Second, nucleon reaction, namely (n, p), (n, α).

Neutrons are absorbed by the nucleus, and the nucleus releases excess energy in the form of non-neutron particles such as protons and alpha particles to reach a relatively stable state—in particle physics and nuclear physics, due to the quantum tunneling effect, helium nucleus 24He can be considered is a whole, the so-called alpha particle.

Three is.

Nuclear fission.

That's right, nuclear fission.

That is, neutrons are absorbed by the nucleus, and the nucleus releases energy in the form of fission into multiple daughter nuclei, so that the daughter nuclei reach a relatively stable state.

Although such reactions often release neutrons, they are still classified as neutron absorption reactions rather than scattering due to the change of the nucleus.

But on the other hand.

Not all 235U absorbing neutrons will undergo fission, for example, 92/235U+ 0/1n[ 92/236U] 92/236U+γ is a radiation capture reaction.

After figuring this out,

All that's left is to have your hands on it.

Extract (n, n), (n, p) and nuclear fission, and then define a concept:

Neutron intensity I.

It represents the number of neutrons vertically passing through a unit area per unit time.

In this way.

The number of neutrons changes during this process:

May scatter back and fail to pass through the target.

It may also be absorbed directly by the target nucleus.

Then this change is expressed as ΔI=σINΔx, where N is the target nucleus density and Δx is the target nucleus thickness.

It can be seen that σ is a probability, which refers to the average probability that neutrons are scattered or absorbed by the target nucleus.

Here we go.

Just add the calculated approximate probabilities together to find the derivative.

Here, look.

The theoretical design of the atomic bomb is about 1/10,000, so easily done, isn't it very simple?

cough cough

At least for Lu Guangda and others, it is still very simple.

So soon.

The entire project team began to calculate in full swing.

"Who will calculate the rationality of the same collision at both ends?"

"Director Hua, the neutron speed after scattering should not produce ultra-high-energy neutrons."

"u(x,t)=z(0)=z(t)=u(xbt,0)=g(xbt)"

"Report, the initial solution has been calculated!"

"mmp, is there anyone going to the toilet together? No one is allowed to go out alone!!"

that's all.

When the time came close to 12 o'clock at night.

Lu Guangda wrote down a final formula:

∫zJ =uhsΣSφD(r,t)+λs/3=limr→04πDA(rL+1)er/L=SA=S4πD. (Late night picture review is not at work, so let's just wait and see.)

After writing.

Lu Guangda wiped the sweat off his forehead and breathed a sigh of relief:

"The nonlinear neutron transport equation is finally calculated."

Note:

Believe me, I have written this process as concisely as possible, and there will be no derivation process later.