Can vacuum be used to store flowing electrons?
The title of the question is:  

Can vacuum be used to store flowing electrons?

Free charged particles like electrons can of course be stored. And of course, this needs a vacuum, since otherwise they would not be free for very long. To store them, they have to be forced on a somehow circular shaped path. Magnetic fields are suitable for this, and they have one interesting property: They deflect moving charged particles, but they don't change their energy. 

The simplest method is a homogeneous magnetic field, where electrons would fly on perfect circles. The faster the particles, the larger the circle. The stronger the field, the smaller.

A more advanced example of this are particle accelerator rings like the Large Electron Positron Collider (LEP) at CERN. This was a ring of 27km circumference, where electrons (and positrons) were accelerated to an energy of 104.5GeV. This can be understood as acceleration by flying through the field of a capacitor charged to 104.5 billion volts. In the beginning, while the ring is filled with packets of electrons / positrons, they are not yet accelerated, just stored. And after acceleration to the desired energy, they are again not accelerated any more, and again just stored in the ring. 

Today, LEP has been replaced by LHC, which does more or less the same with protons. (And 7 trillion volts.)

Another interesting way is to use a magnetic bottle, which consists of an non-homogeneous magnetic field:


Source

The charged particles move on helical paths ans revert their direction when reaching the "bottle necks". However, for a given field configuration, this only works for a limited energy range of the electrons.

Can vacuum be used to store energy in the form of flowing electrons?

(This seems to be the actual question...)

In short: No.

The number of electrons that are "stored" in simple magnetic fields is quite low, so it's no useful energy storage.
Also the LHC (I have no data about LEP) "stores" only about 700Megajoules in the moving protons. A typical household consumes this in less than a month, so it's again not that much energy compared to the large machine.

There are two two reasons why storing energy this way doesn't make sense:


You need to generate the magnetic fields to guide the electrons on their track, and since the electrons repel each other, you also need fields to focus them again. Permanent magnets are not suitable since you need to be able to adjust the fields. But electromagnets need electrical power, even superconducting systems will consume some power somewhere. The energy stored in the electrons would be consumed in (fractions of) seconds by the electromagnets. 
(By the way: In the LHC, the power stored in the magnetic fields is abozt 10x the energy stored in the particles)
Each accelerated charged particle radiates electromagnetic waves. (That's what antennas do). Also an electron on a circular track accelerates permanently (i.e. changes direction), and the waves are called synchroton radiation. (Again: LHC looses about 8MW by this) So, even if you neglect the power consumed by the magnets etc, the moving electrons will loose their energy over time.


The only option is to store resting electrons. There are again inefficient power-consuming methods (e.g. for positrons which should not touch matter) or capacitors.

But you asked for moving electrons...