The best way to overcome your fear is to understand what happens during the donation process.
Plasma is collected through a process called "plasmapheresis." When you come in to donate, a needle is placed in your vein and your blood is pumped into a specialized spinning device that separates the plasma from the other whole blood components, such as red and white blood cells and platelets. While the plasma is collected, the other blood components are filtered into a reservoir. Once the reservoir is full, your red and white blood cells and platelets are returned to your body.
Throughout the process, the system automatically alternates between collection and replacement until the predetermined amount of plasma, based on your weight, is obtained.
The tubing and all other collection supplies that come in contact with your blood are discarded and replaced with new, sterile materials each time a donation procedure is performed.