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in mercury the last orbital?

2006-12-01 00:22:01 · 2 answers · asked by hemanth_b4u1 1 in Science & Mathematics Physics

2 answers

An Alfvén wave in its simplest form is a sine-wave shaped magnetic field variation which acts like a plucked string confined to a plane and carrying attached fluid with it (plasma in this case). In this "plane polarized" case the wave is in the x-z plane and travels along the x-axis. The magnetic field variation (given by b, with amplitude bo, in the figure) is denoted by the solid blue curve, and the plasma variation (given by v) is denoted by the dashed red curve. We see that they are proportional to each other, i.e., b proportional to v. Notice that the background magnetic field, Bo, is considered here to be constant in time and uniform in space throughout the area (actually the volume) of the figure. The total magnetic field (B) is the vector sum of the background field (Bo) and the varying field (b), so that (where Bo, and b are perpendicular to each other): B = Bo + b, (1)
and where b itself is b = bo sin(2pt/T), (2)
and therefore, B = Bo + bo sin(2pt/T), (3)
where we see that the total field, B, is a function of time B(t), even though Bo is not.
Now we consider the value of b (from equation (2) for various t's shown in the top of the figure, where T is the period, and T/4 is a quarter period, etc.:
At t = 1 (meaning at t = 1 x T/4), sin(2pt/T) is sin(p/2) = sin(90ø) = + 1, so b = + bo.
And at t = 2 (meaning at t = 2 x T/4), sin(2pt/T) is sin(p) =sin(180ø) = 0, so b = 0.
And at t = 3 (meaning at t = 3 x T/4), sin(2pt/T) is sin(3p/2) =sin(270ø) = - 1, so b = - bo.
And at also for t = 4 (t = T, not shown in fig), sin(2pt/T) is sin(2p) =sin(360ø) = 0, so b = 0, again, as for t = 2. At t = 5 a full cycle has been completed, and again b= + bo.
The time from t = 1 to t = 3 is a half period, T/2. Then equation (3) gives the following B(t)'s for t's of 1 through 5:
B (1) = Bo + bo, B (2) = Bo + 0 = Bo, B (3) = Bo - bo, B (4) =Bo , and B (5) = Bo + bo.
The first three of these are shown at the bottom of the figure in vector form. If we start with only the uniform field Bo in a uniform plasma and "pluck" the field slightly in some way, like a string on a violin, it will go into such an Alfvén mode where the change in field is perpendicular to the vector Bo. This is called a transverse wave. The wave will move to the right or the left depending on the source of the energy causing the wave. All of these same remarks hold for the velocity, V, so that V = Vo + vo sin(2pt/T), and similar vector diagrams can be drawn for the V's.

2006-12-01 00:27:21 · answer #1 · answered by vivek s 1 · 0 0

Ya, I agree w vivek s. I was just about to say that. ; )

2006-12-01 08:31:16 · answer #2 · answered by GreyGHost29 3 · 0 0

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