So, you've tagged this one
[hard science] which makes it rather hard to answer... especially given definitions like "soup of charged particles at a non-negligible speed(a fraction of C), of polarized(nonpolarized, my bad. I do want the beam to be coherent after all) magnetic dust". I'll spare you a joke about coherency, at least.
The dust remains something of a coherent beam, it expands, but not to the point at which it would be impractical.
Discussions of focussing a beam of pretty much anything onto a plausibly sized starship over interstellar differences are a bit outside of the scope of this question, but you'd do well to consider that "magnetic dust" sounds suspiciously like handwavery to me.
You'd do well to read up on the subject. There's a paper that's well worth reading: Mass beam propulsion: an overview which looks at this specific problem and mentions a few possible solutions. Magnetic dust doesn't appear in any of them, FWIW, but maybe you have a more recent source for that sort of thing?
FWIW, my personal favorite interstellar propulsion proposal is Jordin Kare's Sailbeam which used "smart" projectiles capable of basic aiming at the target ship.
The primary goal of this is to accelerate said ship up to 0.5 C.
This makes things straightforward, though not simple. There's too much energy in any particle travelling at that speed to try and soak it up by letting it collide with the spacecraft. You've got to deflect it some other way, and the usual approach is to use a big magnetic field.
The incoming mass stream is generally assumed to be reduced to ionised gas by some means... self destruction for larger projectiles, collision with a much smaller mass of gas or ionisation via lasers for smaller projectiles. The dust being merely magnetic probably isn't going to cut it here, but this is drifting outside of the scope of the question so I won't go into further detail.
From the Nordley and Crowl paper, here's a diagram of a "dual loop" magnetic reflector:
Note two important things: a stream of plasma shooting forwards through the reflector, and the obvious stream shooting backwards. This has some implications:
- Your ship probably wants to be donut like, to allow undeflected plasma to shoot forwards without the need to shield against all of it. This forward stream of plasma isn't wasted, but helps deflect the interstellar medium in front of you, reducing damage and radiation received by the ship during its journey.
- Your propulsion beam probably wants to be pulsed, or the deflected plasma of particles will interfere with incoming mass. This will reduce the amount of mass hitting the magnetic reflector, hence reducing thrust and efficiency. Fire a blob of propellant, then wait a bit for it to be deflected and for it to dissipate into harmlessness.
There's a further issue here, which is that large and powerful magnetic fields in space induce drag on the spacecraft by interacting with the interstellar medium. This is what ultimately killed the Bussard Ramjet, but does give us the possibility of using a magsail as a sort of interstellar parachute for breaking from relativistic speeds.
To ensure drag forces do not exceed thrust, Kare proposed an larger additional coil with an opposite dipole to to the main thrust-generating reflector coil(s):
- Drag is dominated by low-field region far from
- 2nd larger loop with opposite dipole cancels field
and from the main paper
the the fields do not cancel accurately until well outside the radius of the outer loop
This cancellation loop could have ten times or more the radius of the reflector coils and a much lower current. He doesn't supply a nice diagram of this, but did offer this excellent example of powerpoint art in the presentation that went with the paper linked above:
The diagram is not to scale. The payload here is a point shown in blue, but given that it is at the bullseye of the target it probably isn't recommended for mass-stream driven spacecraft, rather than merely solar wind-driven ones. Note that the payload and cancellation coil are dragged behind the main drive/reflector coil.
To summarise then, and to paraphrase Elijah: the appearance and work of your spacecraft will be as a donut within a donut, possibly within a donut. A very large screening coil to reduce magnetic drag on the interstellar medium whilst the reflectors are operating, and one or two much smaller but higher-current coils making up the reflector. The payload will be distributed around the drive coils, allowing stray propulsion matter to shoot through the middle without needing to be armoured against. The drive coils will still need cooling and shielding, and the payload may need shielding inside a superconducting shell whilst the reflector is operating, depending on whether or not it is something that is unduly affected by strong magnetic fields.