I started with a ship full of max-level veterans, and I'm just a complete noob.

Jiang Ming paused for a moment, his pencil still in his hand.

He stood up, walked to his office, and picked up the microphone.

"teacher."

"Little Jiang."

Qian Xuesen's voice came from the other end, calm and unhurried.

"I've heard about the magnetron."

"The ministry approved the application to establish the research institute this afternoon, as you probably already know."

"understood."

Jiang Ming held the microphone, his fingers hovering over the edge of the receiver.

"Teacher, is this why you called me?"

There was a two-second silence on the other end of the phone.

Qian Xuesen's voice turned somber.

I want to ask you a question.

"Can your magnetron parameters and the sources of your data withstand scrutiny?"

Jiang Ming's breath hitched for a moment.

"Teacher, what data are you referring to?"

"Cavity dimensions, slit width, cathode radius, magnetic field strength."

"If you derived these parameters yourself, then there's no problem."

"But if you heard it from someone else, or saw it somewhere, you'd better think carefully about how to explain it."

Jiang Ming switched the microphone to his other hand.

"Teacher, I did indeed derive it."

"But this derivation path does not directly start from electromagnetic field theory."

There was a moment of silence on Qian Xuesen's end.

"What are you using?"

Fluid mechanics.

"The electron flow in the magnetron rotates at high speed under the influence of orthogonal electric and magnetic fields. Mathematically, this process is equivalent to the peeling of the viscous boundary layer in a variable cross-section pipe."

"I consider the fan-shaped opening of the resonant cavity as the geometric boundary of a fluid conduit, and the momentum conservation equation of the electron flow can be equivalent to the shear force equation of the Prandtl boundary layer."

"Once the critical Reynolds number is calculated, the impedance matching point of the electron flow under a specific magnetic field can be deduced."

There was a long silence on the other end of the phone.

It was so long that Jiang Ming thought the line had been cut off and was about to ask to confirm when Qian Xuesen's voice came through again.

"You're treating electron flow as a fluid?"

"right."

"The rotational motion of the electron cloud in a magnetic field is essentially the collective motion of charged particles in a confined field, which is similar to the laminar transition of fluids in a pipe."

"According to Prandtl's boundary layer theory, fluid near a wall will develop a velocity gradient due to viscosity. When the Reynolds number exceeds a critical value, the flow changes from laminar to turbulent."

"The electron flow in a magnetron is similar. When electrons are emitted at the cathode surface, they are accelerated by the radial electric field and deflected by the axial magnetic field, forming a rotating electron cloud."

"The thickness and rotation speed of this cloud layer depend on the matching relationship between the electric field strength and the magnetic field strength."

"If we consider the electron cloud as a special kind of 'fluid,' then its behavior near the boundary of the anode cavity can be described using boundary layer theory."

Qian Xuesen didn't interrupt, and Jiang Ming continued speaking.

"I assume that the fan-shaped opening of the anode cavity is the variable cross-section boundary of the fluid conduit, and that the electron flow will generate shear stress near this boundary."

According to Prandtl's equation, shear stress is directly proportional to the velocity gradient, which in turn is inversely proportional to the boundary layer thickness.

"Therefore, I can equate the thickness of the electron cloud to the thickness of the boundary layer of a fluid."

"Then the Reynolds number is used to determine the stability of the electron flow."

"The Reynolds number is equal to the flow velocity multiplied by the characteristic length, then divided by the kinematic viscosity."

"For electron flow, the flow velocity is the rotational speed of the electrons, the characteristic length is the radial depth of the cavity, and the kinematic viscosity can be equivalently represented by the electron collision frequency."

"Once I calculate the critical Reynolds number, I can deduce the optimal radius of rotation for the electron flow under a specific magnetic field."

"This radius corresponds exactly to the optimal spacing between the cathode and anode."

"Based on the geometry of the resonant cavity, the radial depth and slit width of the cavity can be calculated, thus obtaining the figure of 8.15 millimeters."

After saying his last sentence, Jiang Ming pressed his finger on the edge of the microphone.

The other end of the phone went silent again.

This silence was longer than the previous one.

Jiang Ming could hear his own heartbeat, each beat striking his eardrums.

About half a minute later, Qian Xuesen's voice rang out again.

"I never thought of that equivalent analogy."

There was a hint of surprise in his voice.

"But from a mathematical perspective, it does make sense."

"Electron flow and fluid are essentially the collective motion of multi-particle systems, and can be treated as equivalent under certain boundary conditions using the continuous medium assumption."

"Your approach is much more ingenious than simply calculating directly from Maxwell's equations."

The sweat on Jiang Ming's palms gradually cooled down.

"Teacher, do you think this derivation path is valid?"

"It can stand firm."

Qian Xuesen's answer was straightforward.

"Not only is it solid, but it's also very creative."

"You've broken down the boundaries between mechanics and electromagnetism, which is a very valuable academic endeavor."

"I will include this idea in the recommendation letter from the high-frequency research lab, so that the relevant ministries can see that we can also conduct original interdisciplinary research in China."

Jiang Ming loosened his grip on the microphone a little.

"Thank you, teacher."

"You're welcome."

Qian Xuesen paused on the other end.

"Xiao Jiang, I have one more question for you."

Jiang Ming's heart jumped again.

"Teacher, please say something."

Did you know about the oxygen-free copper produced by the Shenyang Copper Processing Plant?

Jiang Ming was taken aback.

"As Engineer Fang mentioned today, there's a batch of oxygen-free copper ingots imported during the Soviet aid period, but the right to use them is in the hands of the Soviet expert group."

"right."

Qian Xuesen's voice turned somber.

"That batch of supplies was delivered during the aid construction period in 1950. At that time, Ivanov, the head of the Soviet expert group, signed a storage agreement stipulating that the supplies could only be used for projects designated by the Soviet expert group."

"Now that you're working on magnetrons, you'll definitely need this batch of oxygen-free copper."

"But Ivanov is a difficult person to talk to; he has always held reservations about China's independent research and development."

"You need to be prepared; you might have to discuss the technology with him face-to-face."

Jiang Ming tapped his fingers on the edge of the microphone.

"Teacher, do you mean he will refuse?"

"They might not refuse, but they'll definitely set conditions."

Qian Xuesen sighed.

"Ivanov is a tech-savvy man; he doesn't care about politics, he only cares about whether you have the ability to use these supplies effectively."

"If you can't come up with a technical solution that convinces him, he'd rather keep these copper ingots sealed in the warehouse than release them to you."

Jiang Ming remained silent for two seconds.

"Teacher, I understand."

"It's good that you understand."

Qian Xuesen paused for a moment on the other end.

"There's one more thing I need to remind you of."

"Teacher, please say something."

"Things are getting a bit tense in Shenyang lately. Once your magnetron reverse engineering report is submitted, Ivanov will know about it very soon."

"If he discovers that you are copying Soviet equipment, his attitude will be even tougher."

"So you'd better solidify the technical solution before he realizes it, so that he can't find any fault with it."

Jiang Ming tightened his grip on the microphone.

"Teacher, I will prepare as soon as possible."

"Um."