A question about charged particle in a magnetic field

[T C]

TL;DR Summary

We all know how charged particles in motion behave in magnetic field perpendicular to it. Now, let's choose a molecule from surrounding air at ambient temperature, somehow ionize it and give some velocity and put it into a magnetic field. I want to know what will happen to the random velocity that it already possesses due to its temperature.

Suppose a molecule from our surrounding air (at ambient temperature) is being selected and is ionized. By some mechanical means, some velocity (say 100 m/s) is added to it and it has been put into a magnetic field perpendicular to its direction of motion. We all know how the molecule will behave in the magnetic field. But, my point is, in addition to the 100 m/s velocity "gifted" to it, it already contains some random velocity that is available to it by virtue of its temperature. As for example ,a Nitrogen molecule at 27°C or 300 K is 516.963 m/s. I want to know what will happen to this kinetic energy. Will this just add to "gifted" kinetic energy of the molecule and increase the velocity of the molecule towards the previous direction or something else will happen.
This is just to understand the behavior of a stream of ionized air being released to a magnetic field perpendicular to the direction of motion of the flow. What will happen to a single molecule will be applicable for a stream too.

 

[PeroK]

The motion of a single charged particle in a uniform magnetic field is in general a helix. The component of its velocity in the direction of the field remains constant. And, it moves in a circle in the plane perpendicular to the magnetic field (assuming it has an initial velocity component in this plane).

 

[PeroK]

PS the magnitude of its velocity will remain constant and not change when the field is turned on.

 

[Baluncore]

This is just to understand the behavior of a stream of ionized air being released to a magnetic field perpendicular to the direction of motion of the flow. What will happen to a single molecule will be applicable for a stream too.

https://en.wikipedia.org/wiki/Magnetohydrodynamic_generator
https://en.wikipedia.org/wiki/Magnetohydrodynamics

 

[T C]

@Baluncore, I know about MHD Generators. I just want to know whether they, especially the magnetic part is capable of converting the internal energy of the flew gas too or it just converts the velocity of the flow into useful power. To be more precise, whether the magnetic field will force the random movement of the ionized molecules to be streamlined in a direction perpendicular to magnetic field or they will remain unchanged?

 

[T C]

PS the magnitude of its velocity will remain constant and not change when the field is turned on.

Magnitude can't be changed because that means because energy can't destroyed. I want to know whether the ionized molecules will still contain the random movements or they will become streamlined perpendicular to the magnetic field?

 

[PeroK]

Magnitude can't be changed because that means because energy can't destroyed. I want to know whether the ionized molecules will still contain the random movements or they will become streamlined perpendicular to the magnetic field?

The random movements are due to collisions with other molecules. Those collisions will still take place in a magnetic field. In a uniform magnetic field the motion between the collisions will be helical, rather than linear.

 

[T C]

In a uniform magnetic field the motion between the collisions will be helical, rather than linear

The helical movement will only occur when the direction of motion is perpendicular to the magnetic field. Will there be any helical motion where the direction of motion isn't perpendicular to the magnetic field?

 

[anorlunda]

But, my point is, in addition to the 100 m/s velocity "gifted" to it, it already contains some random velocity that is available to it by virtue of its temperature.

The velocity of a single particle can't be random by definition. Temperature is proportional to the average kinetic energy in the random motion of many particles that collide with each other. A single particle doesn't have temperature, it has kinetic energy. If it never collides with something else, and if it is not subject to external forces, it's velocity continues forever according to Newton's First Law.

Such was the genius of Boltzmann. He discovered the emergent thermodynamic properties of large collections of particles that are not present in individual particles.

 

[PeroK]

The helical movement will only occur when the direction of motion is perpendicular to the magnetic field. Will there be any helical motion where the direction of motion isn't perpendicular to the magnetic field?

Helical motion is the general case. If the component of velocity parallel to the field is zero, you have circular motion. If the components of velocity perpendicular to the field are zero, you have linear motion.

Circles, lines and no motion could all be considered degenerate helices.

 

[Ibix]

The helical movement will only occur when the direction of motion is perpendicular to the magnetic field. Will there be any helical motion where the direction of motion isn't perpendicular to the magnetic field?

No, that'd be circular motion. Helical motion happens when there's a component of initial velocity parallel to the B field. That component is unaffected by the B field, while the components perpendicular to the field rotate.

 

[T C]

If it never collides with something else, and if it is not subject to external forces,

It has the magnetic field. Does that can change its direction of motion? Suppose the the direction of motion isn't perpendicular to the magnetic field but rather at an angle to it.

If the component of velocity parallel to the field is zero, you have circular motion. If the components of velocity perpendicular to the field are zero, you have linear motion.

What will happen if neither of them is zero?

That component is unaffected by the B field, while the components perpendicular to the field rotate.

How the motion will look like then?

 

[Ibix]

What will happen if neither of them is zero?

How the motion will look like then?

A helix, as @PeroK said in the post you quoted.

 

[T C]

Ok. Now, I understand. But, the actual movement is along the axis of the helix. So, ultimately it will look like a number of helical motions having same axis buy varying radius, right?

 

[PeroK]

Ok. Now, I understand. But, the actual movement is along the axis of the helix. So, ultimately it will look like a number of helical motions having same axis buy varying radius, right?

That's not a helix, that's a helter-skelter!

Ah, you mean of it's involved in random collisions, yes.

 

[Ibix]

Ok. Now, I understand. But, the actual movement is along the axis of the helix. So, ultimately it will look like a number of helical motions having same axis buy varying radius, right?

Well, lots of helices having parallel axes. There wouldn't be a bulk rotation around some particular axis, unless there's some carefully constructed non-uniform magnetic field and ion velocity profile that does that.

 

[T C]

Ah, you mean of it's involved in random collisions, yes.

But, such collisions are only possible when the diameter of the rotation would be more than the mean free path, right? And at least it's clear now that the randomness of the motion is less in comparison to the scenario without the magnetic field.

Well, lots of helices having parallel axes. There wouldn't be a bulk rotation around some particular axis, unless there's some carefully constructed non-uniform magnetic field and ion velocity profile that does that.

Yes, that can be understood. But all axis are perpendicular to the direction of the magnetic field. And what about the particles/ions that entered the magnetic field at an angle >180 degree? My common sense tells me that they will go backward and collide with other ions and thus there would be transfer of momentum.
And last but not the least, suppose the ion flow has entered a MHD generator. In that case, the the perpendicular velocity components of the ion velocities will be converted to the electricity and there will be slowing down in the direction perpendicular to the magnetic field. What will happen to the rotational part of the particles/ions?

 

[T C]

I have just done some calculations and found that if the Magnetic field is 3 Tesla, then the radius of curvature would be far greater than the mean free path. So there will be collisions. In a little bit different way, but the ultimate goal would be the same as neutral atoms.

 

[hutchphd]

I have just done some calculations

It is always good to look at the numbers, but I don't see how it makes any difference. Particles moving randomly on various helical paths will not a priori be different from their straight line cousins in this context.

 

[T C]

Not "Various" helical path. All helix have the axis pointed towards the same direction. If the radius of curvature is less than that of the mean free path, there would be little chance of any collision. Collision will occur as the radius of curvature is much much greater than the mean free path. At the specified temperature above, the mean free path is 176.35 nm, while the radius is 0.07 meter, much much higher. By the way, I have considered the magnetic field to be 0.2 Tesla.

 

[hutchphd]

But the size of the helices as well as their centerline positions will be randomly distributed. I think it will not really matter but I applaud putting in the numberrs, obviating the discussion.

 

[T C]

But the size of the helices as well as their centerline positions will be randomly distributed.

All helices have their axis aligned with the magnetic field. What will differ is the radius of rotation and linear velocity as different atoms have different level of energies.

 

[hutchphd]

Correct. But there will be no imparted drift.

 

[T C]

imparted drift

What you want to mean by that?

 

[hutchphd]

I believe that, absent boundary effects, imposition of a uniform magnetic field on randomly moving charges willl induce no preferred instantaneous velocity direction.

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

Thread will remain closed. OP is not very forthcoming about their reasons for these posts, which makes it hard to offer quality technical help.