Are particles accelerated along magnetic field lines?

[GingerCat]

I have a question which puzzled me when I was reading up about auroras. When talking about the interaction of the solar wind and the Earth's magnetic field, the book said that "particles are accelerated along magnetic field lines towards the earth"

That didn’t sound quite right, as I was taught that the force on a charged particle in a magnetic field is always perpendicular to the motion, so the path would be bent into a circle. If there was a component of the velocity parallel to the magnetic field, it would move that way in a helical path, spiralling along the magnetic field lines. That is pretty much what the book said, but this would imply there is no acceleration. The speed of the particles is unchanged, they are just directed to the poles of the Earth.

So I at first assumed that there is no acceleration, and this was just a sloppy choice of words by the author. But I have now read similar statements in several reputable articles, so I start to wonder if there is more to it. I know that magnetohydrodynamics is complicated because the current of all the moving particles will contribute to the magnetic field, but I can’t see how there can be an acceleration mechanism if the force is always perpendicular to the motion. Are the particles picking up extra kinetic energy from some other source?

 

[davenn]

If there was a component of the velocity parallel to the magnetic field, it would move that way in a helical path, spiralling along the magnetic field lines.That is pretty much what the book said, but this would imply there is no acceleration.

yes the particles spiral down the field lines and the spiralling does imply an acceleration
They are accelerating because they are undergoing a constant change in direction
The same way as the moon orbiting around the Earth or the Earth around the sun is under constant acceleration
This is a non-linear acceleration
Acceleration is a vector quantity ie. made up of velocity (not speed) and direction. If either velocity OR direction is changing, you have an accelerationcheers
Dave

 

[A.T.]

They are accelerating because they are undergoing a constant change in direction

The question is about acceleration parallel to the Earth's magnetic field lines.

 

[davenn]

The question is about acceleration parallel to the Earth's magnetic field lines.

the particles are not moving parallel to the field lines
charged particles won't move in a straight line in a magnetic field, their path will be curved

reread the OP's first 2 paragraphs

they spiral along the field lines and down to the Earth's' magnetic poles

Edit and the thread title ...
Are particles accelerated along magnetic field lines?

to which the answer is, Yes

 

[A.T.]

he particles are not moving parallel to the field lines

So what? They could still gain velocity along this direction, or not. That is the OPs question.

 

[ZapperZ]

I have a question which puzzled me when I was reading up about auroras. When talking about the interaction of the solar wind and the Earth's magnetic field, the book said that "particles are accelerated along magnetic field lines towards the earth"

That didn’t sound quite right, as I was taught that the force on a charged particle in a magnetic field is always perpendicular to the motion, so the path would be bent into a circle. If there was a component of the velocity parallel to the magnetic field, it would move that way in a helical path, spiralling along the magnetic field lines. That is pretty much what the book said, but this would imply there is no acceleration. The speed of the particles is unchanged, they are just directed to the poles of the Earth.

So I at first assumed that there is no acceleration, and this was just a sloppy choice of words by the author. But I have now read similar statements in several reputable articles, so I start to wonder if there is more to it. I know that magnetohydrodynamics is complicated because the current of all the moving particles will contribute to the magnetic field, but I can’t see how there can be an acceleration mechanism if the force is always perpendicular to the motion. Are the particles picking up extra kinetic energy from some other source?

If you have a UNIFORM magnetic field in, say, the z-direction, then the particles will not have an increase in its velocity along this direction. It will still experience a force and an acceleration, but not in this direction.

If the field is non-uniform, let's say the field lines squeeze into a bottleneck, then all bets are off because the physics is a bit more difficult to describe than just the simple geometry of the Lorentz force. You can get a gain in speed in the same z-direction, but obviously, because of the curvature of the field lines, not all of them are always parallel to this direction.

So you are correct in thinking that there is no acceleration in the same direction as the magnetic field lines, but sometime article like this plays fast and loose with what they say. This is where having just a little or no knowledge makes for a blissful ignorance. But if you know a bit more physics, like you do, then it makes it confusing.

BTW. I always encourage my students to bring up topics like this, especially when they read it somewhere that simply just didn't click. It shows that (i) they noticed an inconsistency with how they understood things and (ii) they were thinking. I wish you were one of my students. :)

Zz.

 

[sophiecentaur]

No gain in Energy, although the speed could increase. Energy is only gained, afaik, by interaction with Electric Fields.

 

[Khashishi]

In the broad sense of the term accelerate, meaning just some change in velocity, yes.
As ions move towards the poles, the parallel velocity decreases and the perpendicular velocity increases. This is the magnetic mirror effect.
Ions trapped in the magnetic field will tend to bounce back and forth between the poles.