Its like i was born to answer this one
Render of a Interstellar Spaceship of mine, which uses a linear accelerator for thrust (And interstellar refueling)
On the Portals
This is a nitpick but a circle is 1 dimensional, what you mean is a disk.
On the Linear Accelerators
The portal stuff is a bit useless. Like, you dont need a long accelerator to get up to speed. A 1 meter long Wakefield accelerator can induce $10 GeV$ into a particle. Which translates to $0.99631042638c$. Following this equation;
$$v_p = c*\sqrt{1-\left(\frac{1}{\frac{E_P}{m_P*c^2}+1}\right)^2}$$
Where $E_P$ is the Energy in Joule and $m_P$ is the mass of the particle.
If you spice it up a bit to $100 GeV$ the "muzzle" velocity is already $0.999956747967c$. And that is a 10 meter long tube. What big accelerators like the LHC are after is hardly speed. You can make a 100 meter long accelerator that rivals the speed of the LHC. But you know what your 100 meter tube cant match ? The number of particles. Because that is where the issue is. One particle moving at close to the speed of light is fairly useless. You need a lot of them to do much of anything. To accelerate a lot of particles, you need big boy magnets. So even with your portals, a weapon capable accelerator will not be small. It cant be, otherwise you cannot physically accelerate the sheer number of particles fast enough to make anything funny happen.
On the Question
You know, pretty useless. If you are shooting a weapon that fires at almost the speed of light, that little bit of additional energy from Antimatter annihilation really doesn't matter anymore.
To illustrate the point, lets consider the ship from above. That Thruster induces $400 GeV$ per particle. And fires ~$6.5x10^{23}$ particles per second. Which translates to about $0.001 \frac{kg}{s}$. Moving at $0.999997258692c$ or about $299791636.177 \frac{m}{s}$. The Kinetic energy of this exhaust, cannot be estimated with $\frac{1}{2}mv^2$ anymore. Instead we need;
$$E_k = m_0*c^2\left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right)$$
Which works out to $4.2x10^{16} Joule$ Which is about $10 Mt$ of TNT equivalent. And this is why children we are assuming the magical total system efficiency of 99.9999% xD
But, just how much more energy would we get if we converted this Beam into Antimatter ? Well, that is just $E = mc^2$ assuming 100% conversion bla bla bla. Which works out to $0.02 Mt$ of additional energy ON TOP of our $10 Mt$ beam.
As you can see, thats just not worth it. You are significantly better off just making the gun a bit longer and push the energy to say $500 GeV$. That gives you way more bang for your bug.
The Real Weapon
The render above is deceptive. It makes the exhaust look like a tiny baby girl flame. Where as in reality this exhaust would be several light seconds long before you couldn't see it anymore. The colors and apparent shortness is just relativistic effects.
Obviously, standing in such a beam reduces your life expectancy rapidly. Its a bit like the Titan, one moment you exist the next you dont. But this is not the main danger from such a Drive / Weapon. Its the radiation. Particle accelerators like the LHC, my drive or your Portal Gun produce radiation at the end of the day. And this radiation does not stop being angry until it hits something. So unlike normal rocket exhaust, these kinds of weapons are deadly potentially across a solar system depending on the exact numbers.
Its a bit hard to illustrate just how much radiation the weapon you propose would generate. But this radiation is your actual weapon. You can very realistically irradiate an entire planet in a few minutes with anything that powerful. And if you get close enough you can just cause the Atmosphere to undergo thermonuclear fusion. (Hyperbolic).
This is also why this scene from Avatar 2 is so god damn dumb. If you enter an Atmosphere with an Antimatter rocket Engine, the Atmosphere would explode. I did the math a while ago but each of the ISV´s thrusters would produce the equivalent of 100 Mt per second.
More In Depth
So, why do i think you can ditch most of the idea and just use a particle accelerator on its own like the Thruster in the render ?
First, the exhaust would literally be a few Billion degrees hot. So hot that normal matter just cannot exist within it. Which makes it really handy because it is quiet literally impossible to stop. Even a Magnetic field will struggle if the beam hits it perpendicularly.
Second, unlike a normal weapon this remains deadly for a long time. Even if you are light seconds away, the particles are still moving. They are just so far away that the beam has diffused and not really has a temperature anymore. Its just a bunch of really angry particles. Essentially Cosmic rays. These will not only irradiate anything they touch but also physically degrade the matter. In Fusion reactors, something known as Neutron-Induced Transmutation happens. Where Neutrons enter the atoms of the containment chamber and change the atom. Usually this does not happen with charged particles to the same extend. But if the Charged particles move this fast they overcome nuclear binding / repulsion forces and can Transmutate matter. Which weakens materials very quickly and makes them screamingly radioactive.
Your core idea is not bad, and really imo all you need to do is ditch the Antimatter part. With a pure particle accelerator virtually all of the Particles and as such the Radiation moves away from you. So you yourself do not get turned into a mutant. But the moment you interduce Antimatter some of that will Annihilate before it hits the target. Annihilation produces Gamma / X-Rays omnidirectional. So you get hit as well. The dosage might be low but it is just another point against Antimatter for this application.
Powerful enough particle accelerators are perfectly fine long distance weapons on their own.
