[The parts in a sepia background are greatly appreciated bits of invaluable help from Alex Dresner, PhD.]
The RF noise that is associated with a zipper artifact dominates the signal at a specific electromagnetic frequency, such as $63.25$ MHz, and the $x$ or frequency encoding gradient uses a range of frequencies to encode the position in that direction (for all phase encodes), such as $63-64$ MHz, so that $63.25$ MHz would always appear at the same physical location in a given image.
The representation of the artifact on k-space will not be punctual, as in the simple dot in k-space of a spike artifact. Below is a toy example of what k space might have looked like based on a drawing with a vertical line to the left of a circle on the top row. The vertical line represents the final manifestation of the zipper artifact on image space, while the circle is the actual anatomical image we are trying to acquire. The different k-space representations with the artifact (top row), and without (bottom row) are shown on the right column:
Clearly, the artifact is shown in k-space spread across the $x$-axis ($k_x$) - it has to be this way because the line runs vertically from top to bottom, and hence, its reproduction calls for as many horizontal spatial harmonics as allowed by the pre-selected frequency-direction resolution.
That there is not a single spatial harmonic affected in k-space (as is the case with spike artifacts) may seem to contradict the explanation for the zipper artifact: a specific frequency interfering with the data acquisition process. However,
The correspondence is between an electromagnetic frequency and space (image or physical space), not k-space which is a spatial frequency. We use the frequency encoding of spatial position. So a spatial position cannot be viewed if that frequency has corrupt information.
Below this is illustrated as an electromagnetic source of pollution affecting selectively the red voxel contribution to the final signal received by the coil. An EM leak introduced by opening the door of the scanner with the exam in progress would allow an extraneous EM frequency to enter the room. In this example, this contamination source matches the precession frequency of the red voxel in the brain (localized by the position vector $\color{red}{\vec r}$) induced by the magnetic gradients. The sum of the signal generated by two highlighted voxels (red and magenta) changes as a result of the EM contamination altering the red voxel, resulting in a different final signal (in blue) collected by the receiver coil, and discretized into a line of k-space:
The EM leak would change the phase term introduced by the frequency gradient $\color{turquoise}{\nabla G_z}$ at a particular location $\color{red}{\vec r}$ (the red voxel):
$$\mathrm e^{\mathrm i\; \phi(\color{red}{\vec r},t)}=\exp \left( \mathrm i \; \underbrace{\gamma \left( \int_0^t \color{turquoise}{\nabla G_z} (\tau)\mathrm d\tau \right)}_{k(t)} \cdot \color{red}{\vec r} \right).$$
The match between the EM leak and the precession frequency at $\color{red}{\vec r}$ would distort the information contributed by the red voxel - contained in the initial transverse magnetization, i.e. $M_{xy}(\color{red}{\vec r},0)$ - to the final aggregate signal in any given phase step acquisition filling in k-space, i.e. the Fourier transform:
$$ S(t)=\int M_{xy}(\color{red}{\vec r},0) \;\mathrm e^{\mathrm i\; k(t) \cdot \color{red}{\vec r}} \mathrm d \vec r$$
Therefore, the entire line in k space is affected, even as the only non-informative voxel is the red one. Given the identical replication of the frequency gradient at each phase encoding step, it comes as no surprise to expect a vertical artifactual line.
