Guiding Centre, curvature drift (astro phys)

E R^{2}}{m v} Plugging in the given values, we get:v_{gravitational} = \frac{(1.6 \times 10^{-19} C)(0 V/m)(1000 km)^{2}}{(1.67 \times 10^{-27} kg)(3 \times 10^{7} m/s)} = 0 m/sIn summary, we have estimated the grad-B and curvature drifts of a 10 keV ion in the van Allen belts 1000km above Earth's surface in a dipole magnetic field of 100 Gauss. We found that both drifts are equal in this case, and are much larger than the gravitational drift. This is
  • #1
yakattack
5
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Take a 10 keV ion in the van Allen belts 1000km above Earth's surface in a dipole magnetic field of 100 Gauss. Estimate the grad-B and curvature drift if the particle is a proton and compare this drift with the gravitational drift.


3. I know all the formulas needed, but do not know what the B field would be. Do i use spherical co-ords? In which case B would equal ( [tex]\frac{\mu}{4\pi}\frac{2M}{r^{3}}cos\theta[/tex] , [tex]\frac{\mu}{4\pi}\frac{2M}{r^{3}}sin\theta[/tex] , [tex]0[/tex] ) where M is the magnetic moment of the earth? Then put R=([tex]R[/tex] , [tex]0[/tex], [tex]0[/tex] )? Or am i on the wrong tracks entirely? Any hints greatly appreciated.
 
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  • #2


I can assist you with estimating the grad-B and curvature drift of a 10 keV ion in the van Allen belts 1000km above Earth's surface in a dipole magnetic field of 100 Gauss.

First, let's define some variables:

- B: Magnetic field strength (in Gauss)
- R: Distance from the center of the Earth (in kilometers)
- M: Magnetic moment of the Earth (in Am^2)
- q: Charge of the particle (in Coulombs)
- m: Mass of the particle (in kilograms)
- v: Velocity of the particle (in meters per second)
- E: Electric field strength (in Volts per meter)

Now, let's start with estimating the grad-B drift. This is the drift caused by the gradient of the magnetic field. We can use the formula:

v_{grad-B} = \frac{m v^{2}}{q B R}

Plugging in the given values, we get:

v_{grad-B} = \frac{(1.67 \times 10^{-27} kg)(3 \times 10^{7} m/s)^{2}}{(1.6 \times 10^{-19} C)(100 G)(1000 km)} = 1.57 \times 10^{3} m/s

Next, let's estimate the curvature drift. This is the drift caused by the curvature of the magnetic field. We can use the formula:

v_{curvature} = \frac{m v^{2}}{q B^{2} R}

Plugging in the given values, we get:

v_{curvature} = \frac{(1.67 \times 10^{-27} kg)(3 \times 10^{7} m/s)^{2}}{(1.6 \times 10^{-19} C)(100 G)^{2}(1000 km)} = 1.57 \times 10^{3} m/s

As you can see, the grad-B and curvature drifts are equal in this case. This is because the magnetic field strength (B) and the distance from the center of the Earth (R) are the same in both formulas.

Finally, let's compare these drifts with the gravitational drift. The gravitational drift is caused by the difference in mass between the ion and the Earth. We can use the formula:

v_{gravitational} = \frac{
 
1.

What is the guiding centre in astrophysics?

The guiding centre is a concept in astrophysics that describes the average position and motion of a charged particle as it moves through a magnetic field. It is important in understanding the behavior of particles in space, such as those in the Earth's magnetosphere or in the plasma surrounding stars.

2.

How does the guiding centre relate to the curvature drift?

The guiding centre and the curvature drift are closely related concepts. The curvature drift is the tendency of a charged particle to drift perpendicular to the direction of the magnetic field due to the curvature of the field lines. The guiding centre is the point around which this drift occurs. In other words, the guiding centre is the center of the circular motion caused by the curvature drift.

3.

What factors affect the curvature drift in the guiding centre?

The curvature drift in the guiding centre is affected by several factors, including the strength and direction of the magnetic field, the velocity of the particle, and the mass and charge of the particle. These factors can all influence the size and shape of the circular motion and thus the behavior of the particle in the magnetic field.

4.

How is the guiding centre used in astrophysics research?

The guiding centre is a valuable tool in astrophysics research, as it allows scientists to analyze and understand the behavior of charged particles in magnetic fields. It is used in a variety of studies, including those of the Earth's magnetosphere, the solar wind, and the plasma surrounding stars and galaxies. By studying the guiding centre and the curvature drift, scientists can gain insights into the complex dynamics of these systems.

5.

What are some practical applications of the guiding centre and curvature drift?

The guiding centre and curvature drift have practical applications in fields such as plasma physics and space technology. For example, they are used in the design and operation of fusion reactors, where understanding and controlling the motion of charged particles is crucial. They are also important in the development of spacecraft propulsion systems, as well as in the study and prediction of space weather events that can affect satellites and other technology in orbit.

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