## Principles of Operation

### BACKGROUND

In this section, generation of an unbalanced force is discussed. The generation of an unbalanced force is believed to be impossible based on currently accepted physics.

As discussed in the Resonating Cavity section of this website, a radially-symmetric, equatorially-asymmetric resonating cavity can generate a time-averaged net imbalance in the MFF and a time-averaged net imbalance in the EFF. For the radially-symmetric, equatorially-asymmetric cavity, the combined MFF and EFF always yields a zero-value, time-averaged net Lorentz force on the cavity.

#### UNBALANCED FORCE GENERATION IN THE QDRIVE

This section will show that a radially-asymmetric, equatorially-asymmetric resonating cavity can generate a time-averaged MFF that is not counterbalanced by an equal and opposite time-averaged EFF. This imbalance in the combined MFF and EFF yields a time-averaged net imbalance in the total Lorentz force exerted on the cavity. An unbalanced force is generated.

The resonating cavity depicted in Figure 1 below is a QDrive resonating cavity capable of generating a time-averaged linear imbalance in the net Lorentz forces exerted on the cavity by operation of a TM010 EM wave within the cavity. The linear unbalanced-force vector on the cavity of Figure 1 is coincident with the z-axis of the cavity.

There are 60 identical slots located on the bottom plate of the cavity of Figure 1. The slots are located in areas of the resonating cavity that experience strong magnetic fields and weak electric fields.

##### Figure 1

On the top plate of the cavity, above the slots of the bottom plate, Lorentz forces generated on the cavity walls by the magnetic field of the EM wave point in the positive z-direction. On the bottom plate, on areas of the cavity wall located between the slots (called bridges), Lorentz forces generated by the magnetic field of the EM wave point in the negative z-direction.

When operated with a TM010 EM wave, the cavity generates a time-averaged net imbalance in Lorentz forces on the cavity. The imbalance in Lorentz forces occurs because the magnetic-field, Lorentz-force pressure in the positive z-direction on the top plate is greater than the negative z-directed, magnetic-field, Lorentz-force pressure on the bottom plate.

The EFF generated by the TM010 wave operating in the cavity does not counterbalance the positive z-directed MFF. In the areas of the cavity where strong electric fields occur, the cavity is symmetrical with respect to z-directed, electric-field Lorentz forces. The cavity asymmetries occur in areas of weak electric field and strong magnetic field, meaning that the imbalance in EFF generated by these asymmetries (the slots located on the bottom plate) is negligible compared with the MFF imbalance generated by these asymmetries.

In the cavity of Figure 1, the differential in magnetic-field Lorentz forces is not counterbalanced by the differential in electric-field Lorentz forces.  A time-averaged, net-unbalanced Lorentz force is generated on the cavity by operation of a TM010 EM wave within the cavity.

#### A CLOSER LOOK AT THE MFF IMBALANCE

The Lorentz force imbalance generated on the cavity of Figure 1 occurs because electric currents are deflected onto the vertical side walls of the slots of the bottom plate.

Figure 2 shows a cross-sectional-detail view of 2 slots and 1 bridge of the bottom plate, and a top plate section from the cavity of Figure 1. The arrows over the bridge and beside the two vertical walls of the bottom plate depict the direction and magnitude of the magnetic field of the EM wave at those points in the cavity. The circle containing the X depicts the direction (which is into the plane of the page) of the electric current on the walls of the bottom plate (electrons flow in the opposite direction to the electric current flow). The direction of the magnetic field and the direction of the electric-current flow in Figure 2 reverses on all surfaces during the second half of the wave cycle, but the MFF direction remains the same.

On the top plate, the circle depicts the direction of the electric current on the walls of the top plate.  This electric current flows towards the reader.

Some of the electric current flowing on the bottom plate flows along the vertical walls of the slots. Magnetic-field, Lorentz-force pressure exerted on the electric currents on these side walls creates a Lorentz force with a vector direction that is parallel to the xy plane of the cavity. These forces do not oppose the positive z-directed, magnetic-field, Lorentz forces on the top plate.

The arrow above the "z" depicts the positive z-direction (the arrow is not the z-axis).  The z-axis is aligned vertically with the center of the bridge depicted in Figure 2.

##### Figure 2

The negative z-directed, magnetic-field Lorentz forces exerted on the electric current located on the bridge oppose the positive z-directed Lorentz forces exerted on the top plate. When summed over the entire cavity these negative z-directed forces on the bottom plate are less than the positive z-directed forces on the top plate. This imbalance in the time-averaged MFF Lorentz forces on the cavity creates an unbalanced force on the cavity which is not balanced by an equal and opposite EFF.

Commercially available 3-dimensional, numerical-method, EM-field solvers are used to calculate the surface integral. Cannae LLC used HFSS and Analyst software programs to evaluate the proof-of-concept prototype cavity of the QDrive. Further elaboration on numerical-method-analysis techniques is contained in the Proof-of-Concept section of this web site. The reader is encouraged to verify the Lorentz-force imbalance on the QDrive cavity of Figure 1 using numerical-method analysis.

NOTE Magnetic-field Lorentz forces are exerted in the positive z-direction on the top plate. Magnetic-field Lorentz forces are exerted in the negative z-direction on the bottom plate. These two facts are accepted physics and standard calculations in linear-accelerator applications. The innovation of the QDrive is based on the ability of asymmetric features within the QDrive cavity to cause an imbalance in the MFF which is not counterbalanced by the EFF.

#### DISCUSSION OF THE UNBALANCED FORCE

The unbalanced force generated by the QDrive is dependent upon the characteristics of resonating EM waves operating within the radially-asymmetric cavities of the QDrive. A more complete discussion of the differences between propagating EM waves and resonating EM waves is found in Appendix A.

Resonating EM waves have no time-averaged momentum vector. Interference effects of the resonating wave cancel the time-averaged EM wave momentum over the entire field of the resonant wave. The zero-momentum EM wave has energy available to perform work. In linear-accelerator applications, the EM electric-field energy is used to accelerate charged particles. After accelerating a charged particle (and increasing the charged particle's momentum), the EM wave retains a zero net momentum.

In the QDrive, the zero-momentum EM wave energy is used to perform work on the cavity of the QDrive. After each wave cycle, the resonating EM wave energy retains zero momentum and cannot counterbalance the momentum increase of the cavity by a change in EM-wave momentum. The EM wave imparts a momentum change to the cavity in the cavity-wave interaction, but cannot carry away a momentum change from the cavity-wave interaction.  Momentum is not conserved in a QDrive-cavity, EM-wave interaction.

#### OTHER CONFIGURATIONS OF THE QDRIVE

The QDrive depicted in figure 1 uses radially-asymmetric features located in areas of strong magnetic field to generate a linear unbalanced force. Configurations that create other Lorentz-force imbalances are also possible with the QDrive. Figure 1 of the Resonating Cavity section of this web site shows the types of linear and rotational time-averaged, Lorentz-force imbalances that are possible with various QDrive geometries. The asymmetric features that cause the time-averaged, Lorentz-force imbalances generated by the QDrive may be located in areas of strong electric fields and/or strong magnetic fields.

All configurations of the QDrive have patent-pending status.