What is the solar wind. Sunny wind. Facts and theory. Fast solar wind

SUNNY WIND - a continuous flow of plasma of solar origin, spreading approximately radially from the Sun and filling the solar system up to heliocentric. distances R ~ 100 AU. e. C. in. formed when gasdynamic. expansion of the solar corona (see. The sun) into interplanetary space. At high temperatures pax, which exist in the solar corona (1.5 * 10 9 K), the pressure of the overlying layers cannot balance the gas pressure of the corona matter, and the corona expands.

The first evidence of the existence of post. plasma flux from the Sun were obtained by L. Biermann in the 1950s. on the analysis of the forces acting on the plasma tails of comets. In 1957, Y. Parker (E. Parker), analyzing the conditions of equilibrium of the corona substance, showed that the corona cannot be under hydrostatic conditions. equilibrium, as previously assumed, but should expand, and this expansion under the existing boundary conditions should lead to the acceleration of coronal matter to supersonic speeds (see below). For the first time, a plasma flow of solar origin was recorded on the Soviet space mission. apparatus "Luna-2" in 1959. The existence of post. the outflow of plasma from the Sun was proved as a result of many months of measurements on Amer. cosm. apparatus "Mariner-2" in 1962.

Wed S.'s characteristics. are given in table. 1. Streams S. in. can be divided into two classes: slow - with a speed of 300 km / s and fast - with a speed of 600-700 km / s. Fast currents emanate from areas of the solar corona, where the structure of magn. the field is close to radial. Some of these areas are coronal holes... Slow streams of S. to. connected, apparently, with areas of the crown, in which there is a tangential component of magn. fields.

Tab. 1.- Average characteristics of the solar wind in the Earth's orbit

Speed
Proton concentration
Proton temperature
Electron temperature
Magnetic field strength
The flux density of pythons ....	2.4 * 10 8cm -2 * s -1
Kinetic energy flux density	0.3 erg * cm -2 * s -1

Tab. 2.- The relative chemical composition of the solar wind

	Relative content

	Relative content

In addition to the main. components of S. v. - protons and electrons, in its composition also found-particles, highly ionized. ions of oxygen, silicon, sulfur, iron (Fig. 1). When analyzing gases trapped in foils exposed on the Moon, atoms of Ne and Ar were found. Wed relative chem. S.'s composition of century. is given in table. 2. Ionization. state of matter C. corresponds to the level in the corona where the recombination time is short compared to the expansion time Measurements of ionization temperature of S.'s ions of century. allow determining the electronic temperature of the solar corona.

In S. in. there are decomp. types of waves: Langmuir, whistlers, ion-sound, magnetosonic, Alfvén, etc. (see. Plasma wavesSome of the waves of the Alfvén type are generated on the Sun, and some are excited in the interplanetary medium. The generation of waves smoothes out the deviations of the f-tion of the distribution of particles from Maxwellian and in combination with the effect of magn. field on the plasma leads to the fact that S. century. behaves like a continuous medium. Waves of the Alfvén type play an important role in the acceleration of small components of the shock wave. and in the formation of the f-tion of the distribution of protons. In S. in. contact and rotational discontinuities are also observed, which are characteristic of magnetized plasma.

Figure: 1. Mass spectrum of the solar wind. The horizontal axis is the ratio of the particle mass to its charge, and the vertical axis is the number of particles registered in the energy window of the device for 10 s. Numbers with a "+" sign indicate the charge of the ion.

C. stream. is supersonic in relation to the speeds of those types of waves, to-rye provide eff. transmission of energy to S. century. (Alfvén, sound and magnetosonic waves). Alfvén and sound Mach number C .in. in the Earth's orbit 7. When flowing around the S. obstacles capable of effectively deflecting it (magnetic fields of Mercury, Earth, Jupiter, Saturn or conducting ionospheres of Venus and, apparently, Mars), a detached bow shock wave is formed. C. in. decelerates and heats up at the shock front, which allows it to flow around the obstacle. Moreover, in S. century. a cavity is formed - a magnetosphere (intrinsic or induced), the shape and size of a cut are determined by the pressure balance of magn. fields of the planet and the pressure of the flowing plasma flow (see. Magnetosphere of the Earth, Magnetospheres of planets)... In the case of S.'s interaction in. with a non-conducting body (eg the Moon), the shock wave does not arise. The plasma flow is absorbed by the surface, and a cavity is formed behind the body, which is gradually filled with the sulfuric plasma.

The stationary process of corona plasma outflow is superimposed on nonstationary processes associated with flares on the sun... With strong flares, matter is ejected from the bottom. regions of the corona into the interplanetary medium. At the same time a shock wave is also formed (Fig. 2), edges gradually slows down, spreading in S.'s plasma of century. The arrival of a shock wave to the Earth causes compression of the magnetosphere, after which the development of magnes usually begins. storms (see. Magnetic variations).

Figure: 2. Propagation of interplanetary shock waves and ejection from a solar flare. Arrows show the direction of motion of the solar wind plasma, lines without signature - lines of force of the magnetic field.

Figure: 3. Types of solutions to the equation for the expansion of the crown. The speed and distance are normalized to the critical speed v k and the critical distance R k. Solution 2 corresponds to the solar wind.

The expansion of the solar corona is described by the system of equations for the conservation of mass, the moment of the number of motion and the energy equation. Solutions for dec. the nature of the change in speed with distance are shown in Fig. 3. Solutions 1 and 2 correspond to low velocities at the base of the crown. The choice between these two solutions is determined by the conditions at infinity. Solution 1 corresponds to low rates of expansion of the corona and gives large values \u200b\u200bof pressure at infinity, i.e., it encounters the same difficulties as the static model. crowns. Solution 2 corresponds to the transition of the expansion rate through the values \u200b\u200bof the speed of sound ( v to) on some critical. distance R to and subsequent expansion at supersonic speed. This solution gives a vanishingly small pressure at infinity, which makes it possible to match it with the low pressure of the interstellar medium. The course of this type was named by J. Parker by S. in. Critical the point is above the surface of the Sun if the temperature of the corona is less than a certain critical value. meaning , where m is the proton mass, is the adiabatic exponent, and is the mass of the Sun. In fig. 4 shows the change in the expansion rate from heliocentric. distance depending on the temperature of the isothermal. isotropic corona. Subsequent models of S. in. take into account variations in the coronal temperature with distance, the two-fluid nature of the medium (electron and proton gases), thermal conductivity, viscosity, nonspherical. the nature of the expansion.

Figure: 4. Profiles of the solar wind velocity for the isothermal corona model at different values \u200b\u200bof the coronal temperature.

C. in. provides basic outflow of thermal energy of the corona, since heat transfer to the chromosphere, electromagnet. corona radiation and electronic thermal conductivity of S. century. insufficient to establish the thermal balance of the crown. Electronic thermal conductivity provides a slow decrease in the temperature of S. in. with distance. C. in. does not play any significant role in the energy of the Sun as a whole, since the energy flow carried away by it is ~ 10 -7 luminosity The sun.

C. in. carries with it to the interplanetary medium the coronal magn. field. The lines of force of this field frozen into the plasma form an interplanetary magn. field (MMP). Although the strength of the IMF is low and its energy density is approx. 1% of the density kinetic. energy of a semiconductor, it plays an important role in the thermodynamics of semiconductors. and in the dynamics of S.'s interactions. with the bodies of the solar system, as well as S. between themselves. Combination of S.'s expansion. with the rotation of the sun leads to the fact that magn. the lines of force frozen in in S. century have a shape close to the spiral of Archimedes (Fig. 5). Radial B Rand azimuthal components of magn. fields vary differently with distance near the plane of the ecliptic:

where is ang. the speed of rotation of the sun, and is the radial component of the velocity of the superstructure, index 0 corresponds to the initial level. At the distance of the Earth's orbit, the angle between the direction of magn. fields and R about 45 °. At large A magn. the field is almost perpendicular to R.

Figure: 5. The shape of the interplanetary magnetic field line. is the angular velocity of rotation of the Sun, and is the radial component of the plasma velocity, R is the heliocentric distance.

S. century, arising over the regions of the Sun with decomp. orientation magn. fields, forms flows with differently oriented IMF. Separation of the observed large-scale structure of S. of century. for an even number of sectors with diff. the direction of the radial component of the IMF is called. interplanetary sector structure. S.'s characteristics. (speed, temp-pa, particle concentration, etc.) also in cf. change naturally in the cross section of each sector, which is associated with the existence of a fast stream of S. in. inside the sector. The boundaries of the sectors are usually located within the slow flow of S. to. Most often, 2 or 4 sectors are observed rotating with the Sun. This structure, which is formed during S.'s pulling of century. large-scale magn. fields of the corona, can be observed for several. revolutions of the sun. The IMF sector structure is a consequence of the existence of a current sheet (TC) in the interplanetary medium, which rotates with the Sun. TC creates a jump in magn. fields - the radial components of the IMF have different signs on opposite sides of the TS. This TS, predicted by H. Alfven (N. Alfven), passes through those parts of the solar corona, to-rye connected with active regions on the Sun, and separates the indicated regions with decomp. signs of the radial component of the solar magn. fields. TS is located approximately in the plane of the solar equator and has a folded structure. The rotation of the Sun leads to the twisting of the TC folds in a spiral (Fig. 6). Being near the plane of the ecliptic, the observer turns out to be either higher or lower than the TS, due to which he falls into sectors with different signs of the radial IMF component.

Near the Sun in the northern century. there are longitudinal and latitudinal velocity gradients due to the difference in the velocities of fast and slow streams. With distance from the Sun and the steepening of the boundary between the streams in the north. radial velocity gradients arise, which lead to the formation collisionless shock waves (fig. 7). First, a shock wave is formed, propagating forward from the boundary of the sectors (direct shock wave), and then a backward shock wave propagating to the Sun is formed.

Figure: 6. The shape of the heliospheric current sheet. Its intersection with the plane of the ecliptic (inclined to the equator of the Sun at an angle of ~ 7 °) gives the observed sector structure of the interplanetary magnetic field.

Figure: 7. The structure of the interplanetary magnetic field sector. Short arrows show the direction of the solar wind plasma flow, lines with arrows - magnetic field lines, dash-dot line - sector boundaries (intersection of the plane of the figure with the current sheet).

Since the velocity of the shock wave is less than the velocity of the solar velocity, the plasma carries the backward shock wave away from the sun. Shock waves near the boundaries of the sectors are formed at distances of ~ 1 AU. e. and traceable to distances of several. and. e. These shock waves, as well as interplanetary shock waves from solar flares and near-planetary shock waves, accelerate particles and are, thus, a source of energetic particles.

C. in. extends to distances of ~ 100 AU. e., where the pressure of the interstellar medium balances the dynamic. S.'s pressure in. The cavity swept out by S. century. in the interstellar medium, forms the heliosphere (see. Interplanetary environmentThe expanding S. century. together with the magnesium frozen into it. field prevents galactic penetration into the solar system. cosm. rays of low energies and leads to variations in cosmic. rays of high energies. A phenomenon analogous to S. of century has also been found in some other stars (see. Stellar wind).

Lit .: Parker E. N., Dynamic processes in the interplanetary medium, trans. from English, M., 1965; B r and d t J., Solar wind, trans. from English., M., 1973; Hundhausen A., Corona expansion and solar wind, trans. from English, M., 1976. O. L. Vaysberg.

It can reach values \u200b\u200bup to 1.1 million degrees Celsius. Therefore, having such a temperature, the particles move very quickly. The sun's gravity cannot hold them - and they leave the star.

The Sun's activity changes over an 11-year cycle. In this case, the number of sunspots, radiation levels and the mass of material ejected into space change. And these changes affect the properties of the solar wind - its magnetic field, speed, temperature and density. Therefore, the solar wind can have different characteristics. They depend on where exactly its source was on the Sun. And they also depend on how fast the area rotated.

The speed of the solar wind is higher than the speed of movement of the coronal holes. And it reaches 800 kilometers per second. These holes appear at the poles of the Sun and at its low latitudes. They acquire their largest dimensions during those periods when activity on the Sun is minimal. The temperatures of matter carried by the solar wind can reach 800,000 C.

In the coronal streamer belt, located around the equator, the solar wind moves more slowly - about 300 km. per second. It is found that the temperature of matter moving in a slow solar wind reaches 1.6 million C.

The sun and its atmosphere are composed of plasma and a mixture of positively and negatively charged particles. They have extremely high temperatures. Therefore, matter constantly leaves the Sun, carried away by the solar wind.

Impact on Earth

When the solar wind leaves the Sun, it carries charged particles and magnetic fields. The particles of the solar wind emitted in all directions constantly affect our planet. This process has interesting effects.

If material carried by the solar wind reaches the surface of the planet, it will cause serious damage to any life form that exists on. Therefore, the Earth's magnetic field serves as a shield, redirecting the trajectories of solar particles around the planet. The charged particles, as it were, "drain" outside of it. The impact of the solar wind changes the earth's magnetic field in such a way that it deforms and stretches on the night side of our planet.

Occasionally, the Sun throws out large volumes of plasma known as coronal mass ejections (CMEs), or solar storms. This occurs most often during the active period of the solar cycle, known as solar maximum. CMEs have a stronger effect than standard solar wind.

Some bodies in the solar system, like the Earth, are shielded by a magnetic field. But many of them have no such protection. The satellite of our Earth has no protection for its surface. Therefore, it experiences the maximum impact of the solar wind. Mercury, the planet closest to the Sun, has a magnetic field. It protects the planet from normal standard winds, but it is unable to withstand more powerful flares like CME.

When high- and low-speed solar wind streams interact with each other, they create dense regions known as rotationally interacting regions (CIRs). It is these areas that cause geomagnetic storms when they collide with the earth's atmosphere.

The solar wind and the charged particles it carries can affect Earth satellites and Global Positioning Systems (GPS). Powerful surges can damage satellites or cause position errors when using GPS signals tens of meters away.

The solar wind reaches all planets in. NASA's New Horizons mission discovered it while traveling between and.

Solar wind study

Scientists have known about the existence of the solar wind since the 1950s. But despite its severe impact on Earth and astronauts, scientists still don't know many of its characteristics. Several space missions in recent decades have tried to explain this mystery.

Launched into space on October 6, 1990, NASA's Ulysses mission studied the sun at different latitudes. She has measured various properties of the solar wind for over ten years.

The Advanced Composition Explorer () mission had an orbit associated with one of the special points located between the Earth and the Sun. It is known as the Lagrange point. In this area, the gravitational forces from the Sun and the Earth have the same value. And this allows the satellite to have a stable orbit. Started in 1997, the ACE experiment studies the solar wind and provides real-time measurements of constant particle flux.

NASA's STEREO-A and STEREO-B spacecraft study the edges of the Sun from different angles to see how the solar wind is born. According to NASA, STEREO has presented "a unique and revolutionary view of the Earth-Sun system."

New missions

NASA plans to launch a new mission to study the sun. It gives scientists hope to learn even more about the nature of the sun and solar wind. NASA Parker Solar Probe, scheduled for launch ( successfully launched 12.08.2018 - Navigator) in the summer of 2018, will work in such a way as to literally “touch the sun”. After several years of flight in an orbit close to our star, the probe will plunge into the Sun's corona for the first time in history. This will be done in order to get a combination of fantastic images and measurements. The experiment will advance our understanding of the nature of the solar corona, and improve our understanding of the origin and evolution of the solar wind.

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The Sun's atmosphere is 90% hydrogen. Its most distant part from the surface is called the Sun's corona, and it is clearly visible during total solar eclipses. The corona temperature reaches 1.5-2 million K, and the corona gas is fully ionized. At such a plasma temperature, the thermal velocity of protons is about 100 km / s, and of electrons - several thousand kilometers per second. To overcome the solar attraction, an initial speed of 618 km / s, the second cosmic speed of the Sun, is sufficient. Therefore, there is a constant leakage of plasma from the solar corona into space. This flow of protons and electrons is called the solar wind.

Having overcome the attraction of the Sun, the particles of the solar wind fly along straight trajectories. The speed of each particle hardly changes with removal, but it can be different. This speed depends mainly on the state of the solar surface, on the "weather" on the Sun. On average, it is equal to v ≈ 470 km / s. The solar wind passes the distance to the Earth in 3-4 days. In this case, the density of particles in it decreases in inverse proportion to the square of the distance to the Sun. At a distance equal to the radius of the earth's orbit, in 1 cm 3 there are on average 4 protons and 4 electrons.

The solar wind reduces the mass of our star - the Sun - by 10 9 kg per second. Although this number seems large on Earth's scales, it is really small: the decrease in solar mass can be seen only for times thousands of times longer than the current age of the Sun, which is approximately 5 billion years.

The interaction of the solar wind with a magnetic field is interesting and unusual. It is known that charged particles usually move in a magnetic field H along a circle or along helical lines. This is true, however, only when the magnetic field is strong enough. More precisely, for the motion of charged particles in a circle, the energy density of the magnetic field H 2 / 8π must be greater than the kinetic energy density of the moving plasma ρv 2/2. In the solar wind, the situation is the opposite: the magnetic field is weak. Therefore, charged particles move in straight lines, and the magnetic field is not constant, it moves along with the flow of particles, as if carried away by this flow to the periphery of the solar system. The direction of the magnetic field in the entire interplanetary space remains the same as it was on the surface of the Sun at the time of the exit of the solar wind plasma.

The magnetic field, as a rule, changes its direction 4 times when walking along the equator of the Sun. The sun rotates: points at the equator complete a revolution in T \u003d 27 days. Therefore, the interplanetary magnetic field is directed along spirals (see Fig.), And the whole picture of this figure rotates following the rotation of the solar surface. The angle of rotation of the Sun changes as φ \u003d 2π / T. The distance from the Sun increases with the speed of the solar wind: r \u003d vt. Hence the equation of the spirals in Fig. has the form: φ \u003d 2πr / vT. At a distance of the earth's orbit (r \u003d 1.5 10 11 m), the angle of inclination of the magnetic field to the radius vector is, as it is easy to check, 50 °. On average, such an angle is measured by spacecraft, but not very close to the Earth. In the vicinity of planets, the magnetic field is arranged differently (see Magnetosphere).

Figure 1. Helisphere

Figure 2. Solar flare.

The solar wind is a continuous flow of plasma of solar origin, propagating approximately radially from the Sun and filling the solar system up to heliocentric distances of the order of 100 AU. SV is formed during the gas-dynamic expansion of the solar corona into interplanetary space.

Average characteristics of the solar wind in the Earth's orbit: speed 400 km / s, proton density - 6 per 1, proton temperature 50,000 K, electron temperature 150,000 K, magnetic field strength 5 · oersted. Solar wind streams can be divided into two classes: slow - with a speed of about 300 km / s and fast - with a speed of 600-700 km / s. The solar wind arising over the regions of the Sun with different orientations of the magnetic field forms flows with differently oriented interplanetary magnetic field - the so-called sector structure of the interplanetary magnetic field.

The interplanetary sector structure is the division of the observed large-scale structure of the Solar Wind into an even number of sectors with different directions of the radial component of the interplanetary magnetic field.

The characteristics of the Solar wind (speed, temperature, concentration of particles, etc.) also, on average, regularly change in the cross section of each sector, which is associated with the existence of a fast flow of the Solar wind inside the sector. Sector boundaries are usually located within the slow flow of the Solar Wind. Most often, two or four sectors are observed rotating with the Sun. This structure, formed when the solar wind pulls out the large-scale magnetic field of the corona, can be observed during several solar revolutions. The sectorial structure is a consequence of the existence of a current sheet in the interplanetary medium, which rotates with the Sun. The current sheet creates a jump in the magnetic field: above the layer, the radial component of the interplanetary magnetic field has one sign, below it - another. The current sheet is located approximately in the plane of the solar equator and has a folded structure. The rotation of the Sun leads to the twisting of the folds of the current sheet in a spiral (the so-called "ballerina effect"). Being near the plane of the ecliptic, the observer finds himself either above or below the current sheet, due to which he finds himself in sectors with different signs of the radial component of the interplanetary magnetic field.

When the Solar wind flows around obstacles capable of effectively deflecting the Solar wind (magnetic fields of Mercury, Earth, Jupiter, Saturn or conducting ionospheres of Venus and, apparently, Mars), a bow shock wave is formed. The solar wind is decelerated and heated at the shock front, which allows it to flow around the obstacle. In this case, a cavity is formed in the solar wind - a magnetosphere, the shape and size of which is determined by the balance between the pressure of the planet's magnetic field and the pressure of the flowing plasma stream. The shock front is about 100 km thick. In the case of the interaction of the Solar Wind with a non-conducting body (the Moon), a shock wave does not arise: the plasma flow is absorbed by the surface, and a cavity gradually filled with the Solar Wind plasma forms behind the body.

The stationary process of corona plasma outflow is superimposed by non-stationary processes associated with solar flares. With strong solar flares, matter is ejected from the lower regions of the corona into the interplanetary medium. In this case, a shock wave is also formed, which gradually slows down as it moves through the solar wind plasma.

The arrival of the shock wave to the Earth leads to compression of the magnetosphere, after which the development of a magnetic storm usually begins.

The solar wind extends to a distance of about 100 AU, where the pressure of the interstellar medium balances the dynamic pressure of the solar wind. The cavity swept by the solar wind in the interstellar medium forms the heliosphere. The solar wind, together with the magnetic field frozen into it, prevents galactic cosmic rays of low energies from penetrating into the solar system and leads to variations in cosmic rays of high energies.

A phenomenon similar to the solar wind has also been found in some types of other stars (stellar wind).

The flow of energy from the Sun, fueled by a thermonuclear reaction at its center, is fortunately extremely stable, unlike most other stars. Most of it is eventually emitted from the Sun's thin surface layer - the photosphere - in the form of visible and infrared electromagnetic waves. The solar constant (the magnitude of the solar energy flux in the Earth's orbit) is 1370 W /. You can imagine that for every square meter of the Earth's surface there is the power of one electric kettle. Above the photosphere is the Sun's crown - a zone visible from Earth only during solar eclipses and filled with rarefied and hot plasma with a temperature of millions of degrees.

This is the most unstable shell of the Sun, in which the main manifestations of solar activity, affecting the Earth, originate. The shaggy view of the Sun's corona demonstrates the structure of its magnetic field - luminous clumps of plasma are elongated along the lines of force. Hot plasma emanating from the corona forms the solar wind - a stream of ions (consisting of 96% of hydrogen nuclei - protons and 4% of helium nuclei - alpha particles) and electrons, accelerating into interplanetary space at a speed of 400-800 km / s ...

The solar wind stretches and carries away the solar magnetic field.

This happens because the energy of the directed motion of the plasma in the outer corona is greater than the energy of the magnetic field, and the principle of freezing-in entrains the field behind the plasma. The combination of such a radial outflow with the rotation of the Sun (and the magnetic field is "attached" to its surface) leads to the formation of a spiral structure of the interplanetary magnetic field - the so-called Parker's spiral.

The solar wind and magnetic field fill the entire solar system, and thus the Earth and all other planets are actually in the sun's corona, experiencing not only electromagnetic radiation, but also the solar wind and solar magnetic field.

During the period of minimum activity, the configuration of the solar magnetic field is close to dipole and is similar to the shape of the Earth's magnetic field. As the activity reaches its maximum, the structure of the magnetic field becomes more complex for reasons that are not entirely clear. One of the most beautiful hypotheses says that when the Sun rotates, the magnetic field seems to wind on it, gradually sinking under the photosphere. Over time, during just a solar cycle, the magnetic flux accumulated under the surface becomes so large that the bundles of lines of force begin to be pushed outward.

The places where the field lines emerge form spots on the photosphere and magnetic loops in the corona, which are visible as regions of increased plasma glow in X-ray images of the Sun. The magnitude of the field inside sunspots reaches 0.01 Tesla, a hundred times greater than the field of the quiet Sun.

Intuitively, the energy of the magnetic field can be associated with the length and number of lines of force: the higher the energy, the more of them. When approaching the solar maximum, the enormous energy accumulated in the field begins to periodically explosively release, spending on the acceleration and heating of the particles of the solar corona.

Sharp intense bursts of short-wave electromagnetic radiation from the Sun accompanying this process are called solar flares. On the Earth's surface, flares are recorded in the visible range as small increases in the brightness of individual parts of the solar surface.

However, even the first measurements carried out on board spacecraft showed that the most noticeable effect of flares is a significant (up to hundreds of times) increase in the flux of solar X-ray radiation and energetic charged particles - solar cosmic rays.

During some flares, significant amounts of plasma and magnetic field are also ejected into the solar wind - the so-called magnetic clouds, which begin to expand rapidly into interplanetary space, retaining the shape of a magnetic loop with ends resting on the Sun.

The plasma density and the magnitude of the magnetic field inside the cloud are tens of times higher than the values \u200b\u200bof these parameters in the solar wind typical for quiet times.

Despite the fact that during a large flare up to 1025 joules of energy can be released, the total increase in the energy flux at the solar maximum is small and amounts to only 0.1-0.2%.