FLOATING SPARK PLUG AND IGNITION METHOD FOR INTERNAL COMBUSTION ENGINE CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This application claims priority to U.S. Provisional Patent Application No.63/180,842, filed on April 28, 2021, entitled “FLOATING SPARK PLUG,” the disclosure of which is incorporated herein by reference in its entirety. BACKGROUND TECHNICAL FIELD [0002] Embodiments of the subject matter disclosed herein generally relate to igniting a fuel mixture in an internal combustion engine, and more particularly, to an ignition system that has a floating spark plug for igniting the fuel mixture in the internal combustion engine to achieve lean-burn combustion. DISCUSSION OF THE BACKGROUND [0003] The car industry (and other industries that use internal combustion engines) are facing increased regulations on the emission of CO ₂ and NO _x from combustion to cope with the climate change issues. It is expected that governments worldwide will soon ask the car industry to use carbon free (or neutral) fuels only, such as hydrogen, ammonia, and e-fuels if the existing fossil fuel-based engines are not clean enough. However, the efficient use of fossil fuels can also reasonably mitigate the CO ₂ emission. In this light, the lean-burn combustion technology has been considered as one of the ways to allow a smooth transition towards a carbon neutral society.

[0004] Lean-burn combustion technology has been widely used to increase the thermal efficiency of spark ignition (SI) engines. A high thermal efficiency can be achieved mainly through the improvement of both pumping and heat losses. In addition, since the O ₂ contents in the exhaust neutralizes the 3-way catalytic converter, a significant reduction of NO _x emission has to be obtained by lowering a flame temperature with the maximized amount of excessive air.

[0005] Therefore, the ignition has been a challenging issue for the lean-burn SI engines with an extremely lean mixture near the flammability limit. To facilitate the ignition process, various methods have been studied: i) stretched spark discharges using tumble flows, ii) enhanced ignition energy systems, iii) a pre-chamber ignition system, iv) a laser ignition system, v) nanosecond repetitive pulsed discharges, and vi) microwave boosted ignition systems.

[0006] On the other hand, the combustion duration becomes longer due to the substantially decreased laminar burning velocities in lean mixtures. Previous studies using the tumble flows have also shown improved combustion durations, since the highly wrinkled flame area due to the tumble flow results in increased overall burning rates. In fact, the combination of an inductive coil and a spark plug has been a common ignition method in SI engines. Thus, the concept of the stretched spark using a high-speed flow seems to be a practically feasible way of igniting lean mixtures in SI engines, solving issues with both the ignition of lean mixtures and a slow flame propagation. [0007] A bigger ignition kernel can facilitate the ignition as a mixture becomes leaner because the ignition process is related to the minimum quenching distance. The stretched spark channel can consequently promote the ignition by increasing the size of the spark, whereas the ignition probability deteriorates as the restrike phenomenon occurs (shortening of the spark channel as a result of bridging between any two points along the elongated spark). Therefore, the initial stage of a flame kernel, a spark discharge pattern, and the degree of the tumble flow can affect the cyclic variation of the ignition. Although the stretched spark concept has been applied successfully, there is a room for improvement if the underlying physicochemical mechanism is better understood. [0008] Thus, there is a need for a new ignition system and associated method that is applicable to lean-burn combustion to improve the thermal efficiency of the internal combustion engines. The new system is required to extend a lean limit as much as possible to limit the NO _x emission by reducing the flame temperature.

BRIEF SUMMARY OF THE INVENTION [0009] According to an embodiment, there is a floating spark plug for igniting a lean fuel mixture in an internal combustion engine. The floating spark plug includes a single electrode configured to be electrically connected to a voltage source with a proximal end and to apply an electrical potential to a distal end, which is opposite to the proximal end, an insulator configured to electrically insulate the single electrode from an ambient, except for a distal region extending from the distal end, and a body configured to receive part of the single electrode and the insulator, the body being also configured to attach to the internal combustion engine. There is no other electrode except for the single electrode. [0010] According to another embodiment, there is an internal combustion engine that burns a lean fuel mixture. The internal combustion engine a cylinder, a piston located in the cylinder and configured to form a sealed chamber with walls of the cylinder, wherein the piston is actuated to move back and forth inside the cylinder, and a floating spark plug attached to the cylinder and partially entering into the chamber, the floating spark plug configured to generate an arc that ignites the lean fuel mixture. The floating spark plug does not have a ground electrode. [0011] According to yet another embodiment, there is a method for igniting a lean fuel mixture in an internal combustion engine with a floating spark plug. The method includes injecting the lean fuel mixture into a cylinder of the engine, compressing the lean fuel mixture with a piston located in the cylinder, wherein the piston forms a chamber with walls of the cylinder, energizing the floating spark plug, which is attached to the cylinder and partially entering into the chamber, with an electrical potential, generating a corona discharge about a distal end of a single electrode of the floating spark plug due to the applied potential, and forming an arc between the distal end and the piston to ignite the lean mixture. The floating spark plug does not have a ground electrode.

BRIEF DESCRIPTION OF THE DRAWINGS [0012] For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: [0013] Figures 1A and 1B are schematic diagrams of a floating spark plug to be used in an internal combustion engine; [0014] Figure 2 shows the internal combustion engine having the floating spark plug; [0015] Figures 3A to 3C show the formation of a corona discharge followed by the formation of an arc string within a cylinder as a piston moves closer to the floating spark plug; [0016] Figures 4A and 4B illustrate a head of the piston having a ring-shaped notch for anchoring the arc string formed by the floating spark plug and also having a magnet for rotating the arc string; [0017] Figures 5A and 5B illustrate a head of the piston having a crater- shaped dimple for anchoring the arc string formed by the floating spark plug and also having a magnet for rotating the arc string, Figure 5C shows a cylindrical dimple formed in the head of the piston, Figure 5D shows a ring-shaped notch formed to extend from the head of the piston, Figure 5E shows a solid protrusion extending from the surface of the head of the piston, Figure 5F shows the magnet extending outside the head of the piston, and Figure 5G shows the magnet being a disk magnet; [0018] Figure 6 shows the Lorentz force created by the magnetic force generated by the magnet and the current flowing through the arc string; [0019] Figure 7 shows the voltage-current characteristic for the embodiment shown in Figure 2 for a gap of 4 mm; [0020] Figure 8 illustrates the steady voltage across the interelectrode gap and the current for various gaps at an applied voltage of +/- 40 kV; [0021] Figure 9 illustrates the domain of burning states separated by ignition limits depending on the interelectrode gap; [0022] Figure 10 illustrates the lean propagation limit in terms of a jet axis and jet speed for a gap of 2 mm; [0023] Figure 11 is an image of the arc string formed when the jet is present; [0024] Figure 12 illustrates the voltage versus current characteristics with high-speed jet; [0025] Figure 13 illustrates the time evolution of the chamber pressure inside the cylinder of the engine for various air to fuel ratios; and [0026] Figure 14 is a flow chart of a method for igniting a lean mixture inside the engine with the floating spark plug.

DETAILED DESCRIPTION OF THE INVENTION [0027] The following description of the embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. The following embodiments are discussed, for simplicity, with regard to an internal combustion engine that has a single piston and uses propane as a model fuel. However, the embodiments to be discussed next are not limited to a certain number of pistons or to a certain fuel. [0028] Reference throughout the specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments. [0029] According to an embodiment, a novel ignition system has a floating spark plug that initiates the ignition of a fuel-lean mixture in an internal combustion engine. The ignition system is capable of igniting an ultra-lean mixture. The floating spark plug can be retrofitted to an existing internal combustion engine. Different from a traditional spark plug, the floating spark plug has no ground electrode. The spark is generated between a central high-voltage electrode (the only electrode of the floating spark plug) and the head of the piston. For this novel configuration, various parameters of the central high-voltage electrode need to be changed and, in another embodiment, as discussed later, the head of the piston needs to also be changed. All these changes are now discussed in more detail. Note that although each change is presented in a corresponding embodiment, these changes may be combined in any desired way by one skilled in the art, based on the present disclosure. [0030] As illustrated in Figures 1A and 1B, a floating spark plug 100 includes a high-voltage terminal 102 that is electrically connected to a high-voltage electrode 104. The high-voltage electrode 104 may be centrally located within an insulation 106 that prevents an electrical discharge on a side of the electrode. The high-voltage electrode 104, which is the only electrode of the floating spark plug 100, may be made of any conductor material while the insulator 106 is preferably made of a ceramic material. It is noted that the ceramic insulator 106 extends from the high- voltage terminal 102, through a body 108 of the floating spark plug 100, up to a distal region 105 of the high-voltage electrode 104. The high-voltage electrode 104 has a proximal end 104A and a distal end 104B, when referenced to the terminal 102. The proximal end 104A is electrically connected to the terminal 102 while the distal end 104B is freely extending for a given length H from the insulation 106. The electrode 104 extends from the terminal 102 through the body 108 up to the distal end 104A, leaving the distal region 105 completely free of the insulator. The length H of the distal region 105 is different from a common spark plug, as discussed later. In general, the length H is larger for the floating spark plug than a corresponding length (i.e., between the tip of the electrode and the tip of the insulator) for a common spark plug. The body 108 is made of a metal and has an upper part 110 that is shaped as a hex or square or rectangle, and a lower part 112 that has threads 112, which are configured to be attached to an engine. [0031] Different from the traditional spark plug, among other characteristics, the floating spark plug 100 does not have a ground electrode. Thus, the novel floating spark plug 100 shown in Figures 1A and 1B not only misses the traditional ground electrode, but also does not need to be electrically connected to a ground voltage or terminal of a voltage/current/power source. This means that an energy source 120 (e.g., power source or voltage source) is connected with only one lead wire 122 to the terminal 102 and no other electrical connection is provided to the floating spark plug 100, as schematically illustrated in Figures 1B and 2. Note that the source 120 may have a ground lead wire 124, but that lead wire is not connected to the floating spark plug 100. [0032] Figure 2 shows an engine 200 having a cylinder 202 from which the floating spark plug 100 is attached to by threads 112. The cylinder 202 holds a piston 204 that is configured to move up and down relative to the cylinder. The piston forms/define a sealed chamber 203 with the interior walls of the cylinder. Part of the floating spark plug 100 enters inside the chamber 203. This means that if the floating spark plug 100 is not close enough to the piston’s head (top surface) 206, as shown in Figure 2, it cannot generate a spark when an electrical potential is applied to the single electrode 104 by the source 120. Note that because the floating spark plug has a single electrode, only an electrical potential can be applied to the floating spark plug by the source 120. A voltage appears between the electrode 104 and the head 206 of the piston 204. However, the terms voltage and potential are used herein interchangeably given that one skilled in the art would know when a voltage cannot be applied to a single electrode. Only when the piston’s head 206 moves closer to the distal end 104B (or tip portion of the high-voltage electrode 104), then the piston’s head 206 becomes the ground electrode and a spark 220 is generated between the tip portion 104B of the single electrode 104 and the head 204. [0033] Figure 2 shows that the distal region 105 of the electrode 104, which is fully exposed to the ambient, has a length h and this length is related to the specific geometry of the cylinder 202, and to an interelectrode gap g. The interelectrode gap g is defined in Figure 2 as being the distance between the tip 104B of the electrode 104 and the top surface of the head 206 of the piston 204. Figure 2 shows a reference line that corresponds to the top dead center (TDC) at crank angle 0⁰, and this line indicates the position when the piston 204 is at its maximum distance from a center 208 of the crankshaft (not shown) that moves the piston up and down. The distance l + a between the TDC at 0⁰ and the center 208 is defined by the radius a of the crankshaft and the length l of the connecting rod (not shown) that connects the crankshaft to the piston. A distance s between the center 208 of the crankshaft and an instant position of the piston is given by where θ is the angle (i.e., crank angle) between the radius a and a reference direction. When the crank angle is zero the radius a fully extends along the length of the high-voltage electrode 104. [0034] Thus, to avoid an unwanted discharge between the electrode 104 and the edge of the thread 112, a length c of the ceramic insulator 106 is calculated to be at least 2 mm longer than the interelectrode gap g at BTDC at 25⁰, i.e., c > g + 2. In one application, the length c is about 10 mm. In another application, the length c is larger than 10 mm. The interelectrode gap g at TDC at 0⁰ should be less than 1 mm, and this is the maximum interelectrode gap at TDC at 0⁰. The ignition is desired to happen no later than at before TDC (BTDC) at 25⁰, which is shown in Figure 2. Note that BTDC at 25⁰ is characterized by a distance d, which is given by l + a – s(25⁰), which is schematically illustrated in the figure. An interelectrode gap g should be about d + 1 at the moment of spark. Also note that a distance from the end of the insulator 106 to the TDC at 0⁰ is about h + 1 mm. In other words, the tip of the single electrode 104 is located at about 1 mm from the TDC at 0⁰ in one embodiment. [0035] When all these conditions are implemented for the floating spark plug 100, the interelectrode gap g at the moment of spark should be between 1 and d + 1, where the distance d is defined as noted above, and is a function of l, a, and the crank angle θ. The length c of the insulator 106 that extends from the end of the threads 112 toward the tip of the high-voltage electrode 104 is larger than the interelectrode gap g plus 2 mm, and the exposed distal region 105 of the electrode 104 is selected to have a length h such that a distance between the tip 104B of the electrode 104 and the TDC at 0⁰ is about 1 mm. One skilled in the art should understand that all the numerical values used herein can be changed by about +/- 20% without deviating from the scope of the invention. Further, the term “about” is used herein to cover/include this 20% deviation. [0036] With this configuration, the operation of the internal combustion engine 200 is now discussed with regard to Figures 3A to 3C. Figure 3A shows the engine 200 having the piston 204 moving in an upward direction, as indicated by the arrow in the figure. The figure also shows a fuel valve 310 that is configured to allow the fuel 312 (for example, a mixture of air and propane) to enter the chamber 203 defined by the cylinder 202 and the piston 204. When the piston is close enough to the tip 104B of the high-voltage electrode 104, the local field intensity at the tip 104B becomes stronger due to the reduced gap distance g, which results in the so called corona discharge 330, shown in the figure inside the chamber 203. The corona discharge 330 creates a pool of chemically reactive species 331, such as radicals, ozone, and excited state molecules, near the electrode tip 104B. However, at this time the piston is too far from the electrode 104 to form a full spark. As the piston 204 moves closer to the tip 104B of the electrode 104, as shown in Figure 3B, the value of interelectrode gap g is brought into the desired range, i.e., between 1 and d + 1 mm, and the local electrical field intensity at the tip of the electrode becomes even stronger, which results in the corona discharge transforming into the spark 220, which forms between the tip 104B and the head 206 of the piston 204. This means that the floating spark plug 100 uses the head 206 of the piston 204 as the ground electrode during each cycle. This also means that the spark timing is controlled by both the gap distance g and the applied voltage V to the electrode 104. Note that the distance d is dependent on the characteristics of each engine, i.e., l, a, and selected crank angle θ. For this embodiment, the crank angle at which the ignition is initiated has been selected to be about 25⁰. Also note that the values l and a are constants for a given engine. The spark 220 immediately forms an arc string 221. The arc string 221 is a more curved path while the spark is a straight liner path. Due to a high intensity tumble flow (as shown in Figure 3C with a clock-wise arrow 332), the arc string 221 is elongated and stretched. This enlarged volume of hot ignition kernel due to the elongated arc facilitates the ignition of a very lean mixture (air is excessive). The chemically reactive species 331, which were created in the early stage of the corona discharge, promote the flame ignition by supplying radicals to the neighboring mixture near the hot ignition kernel. Thus, this configuration not only achieves a spark generation without a ground electrode attached to the spark plug, but it also achieves a stretched, extended arc string 221, which has the advantage of producing a longer than normal spark, which is a condition for igniting the lean mixture. In other words, the lack of a ground electrode positioned on the spark plug allows the spark to be flexible, i.e., not only to be extended to the piston, but actually to travel within the chamber 203, around a longitudinal axis Z, with the tumble flow, which is precisely what is needed for the ignition of the lean mixture. This extended and travelling spark cannot be achieved with the traditional spark plug that has a fixed ground electrode. [0037] To further enhance the capability of the present engine to burn a lean mixture, which reduces the NOx pollutants, it is possible in one embodiment, as illustrated in Figures 4A and 4B, to control and increase the traveling capabilities of the arc string 221. In this regard, Figure 4A shows the floating spark plug 100 facing the piston’s head 206 and the top surface 206A of the head 206 having a ring- shaped notch 410, centered on the point O where the longitudinal axis Z of the floating spark plug intersects the head 206. The ring-shaped notch 410 may have a depth up to 1 mm into the head 206, and may have a V-shaped cross-section as shown in Figure 4A. However, in another embodiment, the notch 410 may have a square, or rectangular cross-section, or even other shapes or even smaller or larger depths. This feature may be coupled or not with a ring magnet 420 provided into the piston 204, for example, below the top surface 206 of the head 204. In one application, the radius of the ring-shaped notch is about the same as the radius of the ring magnet. The purpose of this novel arrangement is to force the extended arc string 221 to follow a certain path, anchored with an end in the ring-shaped notch 410, and not to let the path of the spark to take a random shape. This happens because the notch 410 intensifies the local electrical field. When the magnet 420 is added, the magnet force drives the extended arc string 221 around the axis Z, to execute the travel described by the arrow 332. [0038] As the piston 204 moves upwardly from the BDC (bottom dead center) position (not shown) in the compression phase, the corona discharge creates chemically reactive species as described above with regard to Figures 3A to 3C. The spark discharge occurs, as the gap distance and the applied voltage are favorable to make the spark (as shown in Figure 3B). The arc string 221 in this situation (see Figure 4B) connects the central high-voltage electrode 104 and one point along a rim of the ring-shaped notch 410 (note that Figure 4B shows the arc string 221 reaching at two points on the ridge 410, but in practice, it is more likely than not that the arc reaches a single point on the rim of the ridge). The arc string 221 rapidly rotates as indicated by the arrow 332, about the axis Z, due to the Lorentz force, which is caused by the interaction between the magnetic field B created by the magnet 420, and the current I present in the arc string 221. The enlarged volume of hot gas created due to the rotating arc string 221 facilitates ignition of the combustible mixture, particularly under fuel-lean conditions. The magnet 420 may be a permanent magnet or an electromagnet. If an electromagnet is used, then it can be turned on and off by a global engine controller to better synchronize the rotation of the arc with the moment when the ignition is desired, or to increase or decrease the rotation of the arc. [0039] Figures 5A to 5C show another possible implementation of a travelling arc string 221. In this embodiment, the ring-shaped notch 410 is replaced by a crater shaped dimple 510 (see Figures 5A and 5B) or a round cylindrical shaped dimple 510 (see Figure 5C), which is formed in the body of the piston 204. Note that the ring-shaped notch 410 preserved the surface of the head 206 within its borders, while the crater/cylindrical shaped dimple 510 removes all the head’s surface area within its borders. A maximum depth of the dimple 510 may be in the order of mm. A radius of the ring-shaped notch 410 and a radius of the dimple 510 may have the same value, i.e., equal to or less than 2 cm. Figures 5A and 5B show that a radius R of the magnet 420 is larger than a radius r of the dimple 510 while Figure 5C shows that the radius R can be equal to radius r. For this case, one end of the arc string 221 engages with the rim 512 of the dimple 510, where the density of the electric field is the largest, and the contact point between the two rotates along the rim 512 based on the Lorenz force. For this case, the arc string 221 may be made to be more inclined (i.e., almost horizontally flat) as the tip 104B of the electrode 104 may be brought very close to or into the surface plane 502 of the surface 206A of the head 206, as shown in Figure 5A. This specific configuration maximizes the Lorentz force acting on the arc string 221. Note that both the embodiments shown in Figures 4A to 5C are capable to effectively control the location of one end of the arc string 221 and also its movement around the axis Z and its speed, in essence being able to control the movement of the entire arc string during the ignition phase. Moving the arc string through the fuel mixture is one reason why a lean mixture can be ignited with this configuration, which is not the case for a traditional ignition engine. [0040] Figure 5D shows another embodiment in which there is a ring-shaped notch 520 that extends/projects out of the surface area 206A of the head 206. For this case, the arc string 221 is formed between the tip of the electrode 104 and the tip of the ring-shaped notch 520. The radius r of the ring-shaped notch 520 may be the same or smaller than the radius R of the magnet 420. The embodiment shown in Figure 5E has a solid protrusion 530, shaped as a round cylinder, that extends from the surface area 206A of the head 206, toward the tip of the electrode 104. The arc string is expected to form between the tip of the electrode and the rim 532 of the solid protrusion 530. The radius r of the solid protrusion 530 may be the same or smaller than the radius R of the magnet 420. [0041] The embodiment shown in Figure 5D may be modified to replace the ring shaped notch 520 with the magnet 420 itself, as illustrated in Figure 5F. In this case, the magnet 420 is partially embedded into the head 206 of the piston 204 and partially exposed to the environment, i.e., located above the surface 206A. For this case, the arc string forms between the tip of the electrode 104 and the rim 422 of the magnet 420. For this embodiment, a trench 424 is formed into the head 206 and the magnet 420 may be glue/welded to the trench 424. A height of the magnet 420 relative to the surface 206A of the head 206 may be selected to be between 1 and 3 mm so that a local electric field is enhanced to form the root of the arc string. Other values may be used. In still another embodiment, as illustrated in Figure 5G, the magnet 420 is not a circular ring, as in the previous embodiments, but rather a disk magnet 420. For this case, the arc string 221 forms between the tip of the electrode 104 and the rim 422 of the magnet 420. While the previous embodiments shown a ring-shaped magnet 420, it is possible that each of those embodiments use a disk magnet or electromagnet. [0042] The capability to control the movement of the arc string is illustrated in Figure 6, which shows the ring-shaped notch 410 or the rim 512 of the crater-shaped dimple 510 (or the rim of the other shapes and elements discussed in the embodiments of Figures 5C to 5G) encircling the point O (see Figure 4A) where the longitudinal axis Z of the floating spark plug 100 intersects the surface area of the head 206. The magnet 420 generates a magnetic field B, which enters into the page in Figure 6 and the arc string 221 is shown extending between the tip 104B of the electrode 104 to the rim 410/510. Note that the arc string 221 acts as a conduit of electrical charges, and thus, as a conduit for the current i. The current is determined by the applied voltage at the tip of the electrode 104 and the voltage should be large enough to electrically breakdown the gaseous member in the chamber 203. The Lorentz force is given by the amplitude of the current i times the amplitude of the magnetic field B and the cosine of the angle between these two vectors. When the current vector lies in the plane of the rim 510, the angle between the two vectors is maximum, i.e., 90⁰, and thus the cosine of this angle is one, i.e., its maximum value. This is the reason that the configuration shown in Figures 5A and 5B can take full advantage of the Lorentz force F. The configuration of Figures 4A and 4B can also take advantage of the Lorentz force F, but only partially as the angle between the magnetic field and current is less than 90⁰. [0043] Further, because the rotation of the arc string 221 is in a steady motion for most of the embodiments, this Lorentz force must be balanced with a drag force acting on the arc string. The drag force can be expressed as F _D =0.5C _D d _arc r _a u ₂ where C _D is a drag coefficient, d _arc is the arc diameter, ra is the ambient gas density, and u is the moving linear speed of the arc. As shown in Figure 5B, the arc shows an angular motion, and thus its angular velocity (w) needs to be considered. In one application, one full turn of the arc string can be considered as a minimum condition to make a large volume of the ignition kernel. Taking a spark duration in IC engine to be around 0.5 ms results in 1 rev./0.5ms, which is about 2000 rev/s. Since the arc length is around a few mm (~ 5mm), the tangential arc moving speed can be ranged up to 10 m/s (= u). Equating Fm = FD, and selecting reasonably estimated values of i = 180 mA, C _D = 0.1 assuming streamlined body, d _arc = 1 mm, and r _a = 10 kg/m ³ for the compression stroke, one can obtain the required B to be around 0.3 T, which can be achieved by using either a permanent magnet or an electromagnet. [0044] The novel floating spark plug 100 facilitates the ignition of ultra lean- burn engines. It is designed to be compatible with conventional engine blocks, and thus, no significant modifications are required. In one application, the floating spark plug requires a higher voltage to be applied than the conventional systems due to the increased gap between the high-voltage electrode and the head of the piston (2 – 4 mm), as compared to the conventional spark plug (1 – 2 mm spark gap). Further, the floating spark plug 100 may require a longer duration for the applied voltage, particularly before making the spark ignition, to create the corona discharges. For the magnetically boosted floating spark plug, the ring magnet needs to be attached underneath the piston head, and additional surface treatment may be required to locally limit the motion of the arc string. [0045] The ultra-lean burn is known to be an effective way of combustion, which can reduce a fuel consumption, thus less CO ₂ emission can be achieved. One of the key challenges for the ultra-lean burn engine is the ignition problem with such a lean mixture, as the conventional spark plug does work anymore. As the mixture becomes leaner, a flame quenching distance becomes larger indicating that a lean flame can be easily extinguished. The ignition process can be thought as an extremely opposite process, thus a larger ignition kernel should be required to ignite a leaner mixture. Therefore, the conventional spark plug with a short arc string of 1– 2 mm is not appropriate for an ultra-lean combustion. In this regard, the floating spark plug is developed to achieve the significantly large volume of an ignition kernel by achieving a longer arc string. Additionally, the corona discharge in the preignition stage creates the pool of chemically reactive species, such as radicals, ozone, and excited state molecules. This significantly improves and extends the ignition quality of the ultra-lean combustion, since the radicals and heat are the most important factors for the combustion chemistry of this type of combustion. [0046] To verify the capabilities of the new floating spark plug, the inventor has performed some experiments as now discussed. The distance between the tip of the electrode 104 and the top of the head 206 was varied between 1 and 13 mm and the voltage applied to the electrode 104 was up to 40 kV. Mass flow controllers supplied propane and air through an injection port into the chamber 203 and the flow rate of the mixture was set up at 24 cm ³ /s for various equivalence ratios Ф, where the equivalence ratio is defined as the ratio of propane to air mixture. The experiments selected one gap g and one equivalence ratio Ф, applied the high voltage (between 10 and 40 kV to the high-voltage electrode 104, repeated this step a couple of time for the same equivalence ratio, then lowered the equivalence ratio by 0.01 and repeated the previous steps until a mixture was found that could not be ignited. Then, the original gap g was changed, and all the above steps were repeated. The effect of a mimicked tumble flow was also investigated. [0047] First, the V-I characteristics of the spark were investigated. For g = 4 mm as an example, the V-I forms are identical regardless of the applied voltage V _a , as shown in Figure 7. As soon as the voltage pulse is applied to the electrode 104, the spark forms at the interelectrode gap g. Then, a significant voltage drop occurs down to 860 V in the order of 60 μs; meanwhile, the current shows a sharp overshoot in the beginning and drops to about 20 mA oscillating for about 6 ms. Then, the current decays to 13 mA, demonstrating a steady behavior onward. Because the power amplifier used in the experiment limited the output current at 13 mA, the resistance created by the spark channel determined the voltage across the interelectrode gap (V _g ). [0048] Similarly, it was found that the current remains at 13 mA, irrespective of the value of the gap g, because this is specific to the power amplifier. Figure 8 shows the representative V _g and I curves, which were measured after the initial transient period for various g and V _a . Regardless of the value of g and the polarity of V _a , the current remains at a value of about 13 mA, while V _g increases as g increases: V _g = 0.6 and 1.8 kV at g = 2 and 13 mm, respectively. The length of the spark is tied with g, and thus, as g increases, the resistance of the spark (R _s ) becomes higher, which explains the increased V _g for the increased g (V _g = I×R _s ). [0049] The inventor also investigated the dependence of the ignition characteristics of the spark on the gap g with particular focus on a lean limit for the ignition resulting in a flame propagation. The inventor used both pressure data and high-speed images to determine the burning state, and as a result, the inventor could identify two burning regimes: i) a complete burning regime with significantly increased pressure and outwardly propagating flames, and ii) an incomplete burning regime with a successful ignition, which only demonstrated the existence of a non- propagating (or very slowly moving) flame near the spark channel and insignificant variation in the pressure. [0050] Thus, the inventor defined the lean propagation limit as the lowest Ф of the complete burning regime for each g, while the lean ignition limit indicates the lowest Ф resulting in a successful ignition of the mixture, which may not necessarily lead to a complete burning. To obtain reference data for the lean limits, the inventor applied a 1-s long voltage pulse for each set of Ф and g. Note that the inventor considered a case as incomplete burning (or no ignition) regime when at least one trial out of three shots showed the incomplete burning state (or no ignition). The critical value of Ф varied by ±0.01, which was confirmed by repeated sets of experiment. [0051] It was found that the extended lean propagation and ignition is limited as g increases. At g = 2 mm, the 1-s long pulse (±40 kV) can ignite mixtures resulting in the complete burning for Ф ≥ 0.71. The polarity of V _a shows no discernable impact on the limit, and Ф = 0.71 can be the lean propagation limit as well as the lean ignition limit as shown in Figure 9. For g = 4 and 8 mm, the polarity of V _a still does not seem to have an effect on the lean propagation limit ( Ф = 0.6 at g = 4 mm, Ф = 0.56 at g = 8 mm). However, from g = 10 mm onward, the negative V _a further extends the propagation limit (solid triangle symbol, Ф = 0.51 at g = 10 mm and Ф = 0.50 at g = 13 mm) as compared to those for the positive V _a (solid square symbol, Ф = 0.55 at g = 10 mm and Ф = 0.54 at g = 13 mm). For a case when Ф decreased below the lean propagation limit for g ≥ 4 mm, it was found the incomplete burning regime even with a successful ignition down to the ignition limit (solid circle symbol). Note that the ignition limit for g ≥ 8 mm corresponds to the lean flammability limit of propane (Ф = 0.41). Also note that the gap g can be selected to be between 2 and 13 mm. [0052] The inventor also measured the minimum energy for the lean propagation limit by changing the duration of the applied pulse. The energy input, E _p , varies from 232 to 5100 mJ in a tested range of g (2–13 mm). The propagation limits for a fixed E _p also indicate the promoting effect of the negative V _a as well as d (see Figure 9). The inventor investigated the lean propagation limit for the fixed E _p at 200 mJ (±10), which was based on a typical E _p in SI engines. Similar to the case with the 1-s long pulse, an increased g extends the lean propagation limit as shown in Figure 9. Up to g = 8 mm, no visible differences due to the polarity of V _a can be found; however, for g = 10 and 13 mm, V _a = –40 kV further lowers the lean propagation limit (open triangle symbol) from those with V _a = 40 kV (open square symbol). At g = 13 mm with V _a = –40 kV for instance, it is necessary to put E _p = 5100 mJ to achieve the complete burning state with the leanest mixture (Ф = 0.5), while for E _p = 200 mJ (only 4% of 5100 mJ) can effectively burn the mixture of Ф = 0.53. [0053] The inventor also investigated the effect of a high-speed jet on the ignition, mimicking the tumble flow pattern occurring in the engine 200 as schematically illustrated by arrow 332 in Figure 3C. During the experiments, the position of the jet relative to the axis Z was varied to have the values z _j = 0.5, 1.0, and 1.5 mm along the 2-mm interelectrode gap g. An energy of E _p = 200 mJ was applied at V _a = –40 kV and investigated the lean propagation limit in terms of z _j and u _j , where the last quantity is the speed of the flow. [0054] The high-speed flow basically helps to extend the lean propagation limit for the case of g = 2 mm as shown in Figure 10. The high-speed jets lower the lean propagation limit significantly from Ф = 0.73 to a range of 0.58–0.6 even at u _j = 3 m/s. However, the effect of an increased speed u _j on the limit is marginal; almost four folds increase in u _j , i.e., at u _j = 11 m/s, whereas the limit improves only down to Ф = 0.57–0.58. In addition, for the cases at z _j = 0.5 mm, the V _a = 40 kV was applied to examine the effect of polarity of V _a on the limit. The limits are Ф = 0.6 and 0.59 at u _j = 3 and 11 m/s, respectively (see Figure 10), which are richer than those with a negative V _a . This indicates a strong effect of the polarity even with the high-speed jets. [0055] The overall improvement due to the high-speed jet can be mainly attributed to the elongated spark length caused by the convection due to the high- speed flow. Therefore, the somewhat insensitive nature of the lean propagation limit with the increased u _j may be correlated with the similar insensitive trend of the lean propagation limit with the increased g as shown in Figure 9. [0056] The discharge image shown in Figure 11 confirms the elongated arc string 221’s length due to the high-speed jets (z _j = 0.5 mm and u _j = 7 m/s in this figure). The increased V _g due to the high-speed flow as in the V-I characteristics shown in Figure 12 also demonstrates the increased spark’s length, because V _g can be a characteristic value for a specific spark length as shown in Figure 8. For the same u _j = 3 m/s, the inventor found a longer spark length as the jet is situated closer to the bottom electrode (lower z _j ). The high velocity zone near the surface of the bottom electrode effectively pushes the spark’s root away from its original position. For the increased u _j at the fixed z _j = 0.5, the inventor found an increased spark length due to a high convectional transport. [0057] The high-speed flow causes a fluctuation of the spark’s root on the bottom electrode. This fluctuation can be seen as the fluctuating V _g in Figure 12. The restrike phenomenon occurring in the conventional spark plug with a high tumble flow is known to deteriorate the quality of the ignition. However, the fluctuation of the spark length did not seem to have a negative effect on the ignition up to u _j = 11 m/s as shown in Figure 10. [0058] The effects of the spark length, polarity of V _a , and high-speed flow on the overall combustion duration were also investigated for the novel floating spark plug 100. The measured chamber pressure traces the progress in combustion, and reaching its peak indicates a complete burning of the mixture inside. In this regard, the pressure data for various conditions inside the engine are shown in Figure 13. It is noted that the combustion durations with the larger spark gap (g = 13 mm) significantly improve as compared to those with the smaller spark gap (g = 4 mm), particularly demonstrating a superior performance with the negative V _a (–40 kV at g = 13 mm). The combustion durations at g = 4 mm are very similar for both polarities showing the elapsed time for the pressure peak, t _p = 68 ms. However, at the higher g (= 13 mm), the combustion duration improves to t _p = 57 ms at V _a = 40 kV and even better at V _a = –40 kV, exhibiting t _p = 51 ms. [0059] This enhanced combustion speed with the larger g can be attributed to the aforementioned early ignition characteristics at the cathode as well as the larger size of the ignition kernel as compared to that with the smaller g. Thus, it is possible to conclude that a larger gap g not only extends the lean propagation limit but also improves the combustion duration. [0060] The high-speed flow facilitates the combustion speed by increasing the flame area due to the turbulence. For the case at z _j = 0.5 mm with g = 2 mm and V _a = –40 kV (see Figure 13), it was found the enhanced combustion duration as u _j increases: t _p = 53, 48, and 43 ms for u _j = 3, 7, and 11 m/s, respectively. Thus, the combustion speed with the tumble flow at u _j = 11 m/s is the best among those tested. Note that for the case at z _j = 0.5 mm and u _j = 11 m/s with g = 2 mm and V _a = –40 kV, the lean propagation limit is Ф = 0.57, which is richer than that (Ф = 0.53) with g = 13 mm and V _a = –40 kV for the same E _p = 200 mJ in the still mixture (see Figure 9). [0061] It is noted that the polarity effect for the combustion speed can be diminished as the effect of the turbulence overrides it. The combustion duration at V _a = 40 kV with the tumble flow at u _j = 11 m/s shows a very similar value as compared to that at V _a = –40 kV. Thus, it is possible to conclude that the high-speed flow promotes the overall faster combustion, and the effect of the polarity on the combustion duration in the presence of the high-speed flow is negligible, while it results in a notable difference for the lean propagation limit as previously mentioned with regard to Figure 10. [0062] The above discussed embodiments defined a border between two successful ignition regimes - a complete and an incomplete burning regime - as a lean propagation limit in terms of the equivalence ratio of a propane/air mixture at a specific interelectrode gap for the spark. It was discovered that the lean propagation limit was extended as the interelectrode gap increased, due to a larger initial kernel size. It was also discovered that, for a longer spark channel, an early ignition occurred near the cathode. Thus, depending on the configuration and shape of electrodes, the polarity of the applied voltage may have an effect on the combustion duration as well as ignition. [0063] The longer spark channel/string also improved the combustion duration, since the area of a propagating flame was larger for the longer spark. The polarity of the applied voltage also played a role in further promoting the combustion duration at a larger interelectrode gap (≥ 10mm). The effect of the high-velocity jet blowing through the interelectrode gap was also investigated, mimicking a tumble flow in an SI engine. As a result of the convectional transport, it was found an elongated arc string, resulting in an extended lean propagation limit as the jet velocity increased and the location of the ejection became closer to the surface of the disk electrode. Due to the turbulence caused by the jet, the wrinkled flame surface also enhanced the combustion duration. Note that in all the experiments performed herein, the jet was used as a substitute for rotating the arc string with the magnet shown in Figures 4A to 5B. In particular, these findings can further stabilize the operation of a SI engine, since the present configuration with a tumble flow did not show the restrike phenomenon observed in a conventional spark plug. [0064] A method for igniting a lean mixture in the internal combustion engine 200 with the floating spark plug 100 is now discussed with regard to Figure 14. The method includes a step 1400 of injecting the lean mixture into a cylinder of the engine, a step 1402 of compressing the lean mixture with a piston located in the cylinder, wherein the piston is actuated to move back and forth inside the cylinder, a step 1404 of energizing the floating spark plug, which is attached to the cylinder and partially entering into the chamber, with a voltage, a step 1406 of generating a corona discharge about a distal end of a single electrode of the floating spark plug, and a step 1408 of forming an arc between the distal end and the piston to ignite the lean mixture. The floating spark plug does not have a ground electrode. In one application, a magnet is provided in the head of the piston so that the formed arc string rotates due to the Lorentz force. [0065] The disclosed embodiments provide a floating spark plug that can be retrofitted to an internal combustion engine to facilitate the ignition of a fuel lean mixture, particularly in ultra-lean burn internal combustion engines. It should be understood that this description is not intended to limit the invention. On the contrary, the embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention as defined by the appended claims. Further, in the detailed description of the embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the claimed invention. However, one skilled in the art would understand that various embodiments may be practiced without such specific details. [0066] Although the features and elements of the present embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein. [0067] This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims.